Electrical – Considering doing a 100A sub panel install on the own. Any guidance would be much appreciated

I can tell you right now that that liquidtight is too small for what you want to do

The AC installer likely ran either 1/2 or 3/4" for the LFMC, depending on the size of the circuit. That's going to be no good for the fat wires you're running, which require 1" for sure if not 1.25" or larger.

Never fear, aluminum's here!

For wires this size, furthermore, using that 3/3/3/5 copper SER cable is an absolute waste of money, atop being a nightmare to wrestle down an extended run of conduit and gobbling up 420mm2 of fill with the grossly oversize neutral and earth wires. Instead, I'd transition from cable to conduit at a junction box located where you plan to exit the crawlspace -- the cable in the crawlspace can be a 1/1/1/3 aluminum SER, which is 1/3rd of the per-foot price, and then the wires in the conduit can be a pair of 1AWG aluminum XHHW-2s for the hots, with 8AWG stranded copper THHN/THWN-2 for the neutral as per 215.2(A)(2) and a bare 8AWG stranded copper wire for the ground as per table 250.122. This gets you a fill of 215mm2 (90*2=180mm2 for the hots, 24mm2 for the neutral, and 11mm2 for the ground), or half of what you'd be pulling through the conduit if you tried to stuff that overpriced cable down it. For ease of pulling reasons, of course, oversizing the conduit from the 1" minimum the aforementioned fill number requires is a very good idea -- 2" flex or LFMC is not out of place here, although it will require a reducing fitting where it enters the box at the house end most likely.

As to all that ooga-booga surrounding aluminum wiring burning your house down? Fat aluminum wires are terminated onto set-screw type lugs that don't have nearly as many problems as receptacle screws and wirenuts (provided they're torqued correctly of course), while modern aluminum wiring is made using a family of alloys dedicated for building wiring applications (AA-8000 series) instead of being the old, finicky EC grade stuff that got the bad rap.

The one precaution you really should (or must, if your AHJ is up-to-date on Code, even) take, though is torquing the lugs to manufacturer's labeled specifications with an appropriate torque wrench or torque screwdriver. This is a new Code mandate for 2017, specified in 110.14(D), and an especially good precaution for aluminum anyway, because it tends to be less forgiving of mistorqued lugs than copper is.

You have the trench depth about right, but simply slap a fat pipe here and call it done.

Putting the short trench at 18" of cover will work (this means you'll probably want to trench to 24" so that there's room for the conduit itself), and you'll want to simply use 2" schedule 80 PVC for this (and the entire run). Don't forget the expansion fittings, though! Also, prefab wide-sweep elbows are a good idea for the transition bends between aboveground and underground, as well as the final bend before you reach the junction box.

That way, if you want to put in fatter wires when you put the Tesla charger in, you have the space to do so instead of having to go back and dig up the conduit, which is quite costly compared to simply buying fatter conduit to begin with.

Don't bother trying to stuff cables through a conduit

For the branch circuits running out to the NEMA box, I'd use individual THWN-2's instead of cables -- again, stuffing cable down conduit's going to leave you swearing more than you have to, especially with the 2 90deg sweeps needed for the underground run (the surface turns can be made using a LR and a LL body). You'll be needing three 6AWG THWN-2 wires (33*3 = 99mm2 fill) for the NEMA 14-50 that the JuiceBox plugs into, two 12AWG THWN-2 wires (9*2 = 18mm2 fill) for the 20A utility receptacle, and a 10AWG bare ground (7mm2 fill) for grounding the whole kit and kaboodle (both circuits in the conduit can share it).

The outdoor receptacles need to be GFCI protected, it doesn't matter where the GFCI is

The GFCI protecting the outdoor receptacle(s) can be part of the receptacle, in the panel, or somewhere in between -- the Code simply states that it needs to be protected, and doesn't care about where you put the GFCI. Putting them in the panel can be advantageous in that the wire run between the panel and the receptacle is protected, and that the GFCI is going to be better sheltered in a panel than in a receptacle box.

Don't forget drainage!

One important point with outdoor electrical enclosures (NEMA boxes, junction boxes, panelboard cabinets, and the likes) is that they must be drained -- not only does condensation or any other moisture that gets in need to exit, you need a way for pressure equalization between "inside the box" and "outside the box" to happen to prevent air pressure differences from driving water across the seals, leaving your "weathertight" NEMA 3R not so able to withstand the weather. This is explicitly permitted in the NEC for drain holes not larger than 1/4" by 314.15:

314.15 Damp or Wet Locations. In damp or wet locations, boxes, conduit bodies, and fittings shall be placed or equipped so as to prevent moisture from entering or accumulating within the box, conduit body, or fitting. Boxes, conduit bodies, and fittings installed in wet locations shall be listed for use in wet locations. Approved drainage openings not larger than 6 mm (1/4 in.) shall be permitted to be installed in the field in boxes or conduit bodies listed for use in damp or wet locations. For installation of listed drain fittings, larger openings are permitted to be installed in the field in accordance with manufacturer's instructions.

As to your schematic and panel selection

There are a few issues with your choices of parts for this project, and I'll address them in turn, starting at the main panel and going downstream.

First off, there just isn't enough volume in a volume marked conduit body (the only ones you can splice in) for what you want to do with that first LB, which is why I suggested an actual box there instead. Of course, if you wish to have the box completely inside, you can use a LB to send the conduit run around the bend and then go into the box.

Second, you'll have to consider fill derates (4-6 current-carrying conductors in a conduit forces an 80% derate on you) when you put the A/C wires in the same run as the feeder. This may force a bump of the feeder hot wires to 1/0 aluminum, which adds to cost and space, as well as re-running the A/C wiring adding to your labor compared to running the new conduit in parallel with the existing run.

Third, that 1.25" PVC is probably not enough of an oversize to be a practical pull over that long stretch (even with conduit bodies to break up the bends), and following the existing run would break the 360deg limit on bends between pull points, in addition to the next-to-last bend being rather too tight (even for 1/2", you need 4" of radius-to-centerline minimum for a legal conduit bend). Using a LB instead of that next-to-last bend would fix both issues with the bend rather nicely. The first two bends in the run can also be replaced with bodies, but you need a LL and a LR for that instead of two LBs due to access issues. As to the conduit size and type? I'd go up to 2" if possible, or 1.5" at a bare minimum, and rigid schedule 40 offers no advantage here over LFMC while requiring more tooling to work with, as well as expansion fittings to keep the run from doing the worm on you.

Next up -- running 2" schedule 80 straight into a FS box (aka weatherproof conduit box) isn't going to work. You're better off using another T body there with a reducer to a more appropriate size to feed the FS, and then just running more 2" schedule 80 off to the NEMA box.

Now that we have all the concerns about conduit selection out of the way, I can tell you right now that you have the wrong panel for the job. That "3" before the "125" in your panel's model number means it's a three phase panel. While you theoretically could use it on a split-phase system, it'd be a waste of a full third of the spaces, which aren't in abundance on a 12 space panel anyway. For the same price, you can get a Siemens PW1624L1125CU instead, which gets you twice as many usable spaces (16 vs 8) and factory fitted grounding bars as well, which is quite helpful for a subpanel.

Inside the panel, you can use GFCI breakers to protect the GFCI'd circuits -- this lets you mount ordinary weather-resistant receptacles in the NEMA box, as well as in the weatherproof box at the other end of the fence. If some "home inspector" can't wrap their heads around a GFCI breaker, that's on them, not you.

As to the wires, while you can go smaller with the copper (2AWG or 3AWG copper vs 0AWG or 1AWG aluminum, depending on if you're invoking the derate rules or not), that doesn't gain you anything compared to aluminum save for a bigger hole in your pocketbook. Keep in mind that loadcenter lugs are tin or zinc plated aluminum anyway, so even on a copper buss loadcenter, it's copper that poses any dissimilar metals problems, not aluminum. Last but not least, you have to put the conduit together first and then pull the wires through it to keep the insulation on the wires from being ripped up excessively by sharp conduit edges -- this is codified in NEC 300.18(A):

(A) Complete Runs. Raceways, other than busways or exposed raceways having hinged or removable covers, shall be installed complete between outlet, junction, or splicing points prior to the installation of conductors. Where required to facilitate the installation of utilization equipment, the raceway shall be permitted to be initially installed without a terminating connection at the equipment. Prewired raceway assemblies shall be permitted only where specifically permitted in this Code for the applicable wiring method.

As to that reroute...

While 800.133 prohibits having that Ethernet cable in the same conduit as mains wiring, what you can do is route the conduit for the feeder alongside the conduit for the Ethernet without having to worry too hard about bothersome EMI. That, and simply use schedule 80 everywhere -- it's probably not worth switching back and forth, especially given that schedule 80 is going to hold up to little oopses like getting weed-whacked or mower-bumped better than schedule 40 will.