You can do it -- you'll need a subpanel loadcenter in a NEMA 3R enclosure, though, as well as watertight conduit/raceway and fittings for the outdoor runs, which will be done using THWN in the conduits.
You will want to put a 30A 2pole for the dryer and a 20A GFCI for the laundry outlets, as well as a spare 20A breaker (if you want a lighting circuit there, or an extra laundry outlet circuit) in your subpanel, which does not need a main breaker of its own, so it can be a four-slot NEMA 3R loadcenter, such as an Eaton BR48L125RP with a GBK10 ground bar in it, as the neutral and ground will be on separate, isolated bars in the subpanel.
As to the feeder breaker, the NEC calls for 1500VA for the laundry outlet circuit (220.52(B)) and a minimum of 5000VA (a 20A dryer) or the wattage of the dryer (whichever is higher) for an electric dryer load (220.54). Assuming your dryer pulls the full 30A (7500VA) and you have 1500VA of laundry circuit load, this yields 9000VA or 37.5A, which requires a 40A feeder breaker in the main panel, and 8AWG THWN for the feeder wires. In reality, your dryer can't sit there and pull 30A continuously without tripping your breaker, so this is a conservative calculation.
Does the sub-panel seem over loaded? If so, I could keep the water-heater in the main panel and free up space in the panel another way.
Seems reasonable to me. Most of the equipment won't draw anywhere near the overcurrent rating, at least not during normal operation. Motor loads will draw a higher current on start, but you shouldn't have a problem.
I know I need four-strand wire to run to the sub-panel (2 hot, neutral, ground) but copper or aluminum and what gauge?
You can use either copper or aluminum, though I recommend copper for DIYers. Copper is quite a bit more expensive, but it's easier to work with (in my opinion). If you feel confident working with aluminum conductors, you can save some money using it.
I've covered the topic of feeder sizing here, so I won't go into detail. If you're using copper, you'll want to use 3 AWG conductors. If you choose to use aluminum, you'll need 1 AWG conductors.
If you want to run a single cable, instead of individual conductors in conduit. You can buy what's called 3-3-3-5 SER cable (1-1-1-3 for aluminum), which will contain three 3 AWG conductors (hot,hot,neutral) and a 5 AWG grounding conductor.
When I run the wire along the floor joist, does it need to be secured to the joist or can it just hang there and rest on the drop ceiling? Seems like it should be secured to the joist with wire hanger or something.
You'll have to attach the cable to the joists, using 1 - 1 1/4" staples or other approved means. Check the packaging, to make sure they are rated for the size cable you're using.
What are the things about this project that I don't know that I don't know. :) These are the scary things IMO...i.e. the questions I don't know enough to ask.
The cable you'll be working with is thick and heavy, and it's not going to be fun pulling it. You'll probably want a couple helpers, to help you wrangle it.
Make sure all your connections are tightened to the manufacturer's specified torque.
If you choose aluminum conductors, make doubly sure you tighten the connections. And don't forget the anti-oxidant.
Come back a day or two after the panel has been put into service, and tighten any connections that need it.
Don't forget to remove the bonding jumper between the grounded and grounding bus bars.
You'll need clamps big enough for the cable, to secure it to the panels.
should I put a 100 amp breaker in the sub-panel to act as the "main" for the sub-panel? Or is the 100 amp breaker in the main panel sufficient?
You can usually pick up a main breaker panel, for about the same price as a main lug only (MLO) panel. In my opinion, unless the secondary panel is next to; or within sight of, the main panel. You're better served to install a main breaker panel. It simply offers better protection during maintenance, or other work within the panel.
For example. If you turn off the feeder breaker in the main panel, and start working in the secondary panel. Somebody could easily come along, and flip on the feeder breaker. Since you can't keep an eye on the breaker, you can never be sure the panel will be dead. (unless of course you're using a lockout like you should).
If the secondary panel is in a separate building or structure, then you either need a main breaker, a main disconnect, or the ability to disconnect all ungrounded conductors within 6 or less hand moves.
Best Answer
At first blush, this would appear to be a Federal Pacific panel in fairly urgent need of immediate replacement due to known-defective breakers and even bigger issues with the buses themselves (if it was just breakers, those could be swapped, a-la Challenger). However, I see from the sticker that you're in Canada. FPE is a somewhat different deal there. I would still be making plans to replace this panel not least, because it's full, but not quite the same urgency as in the US.
Every breaker in this panel is a "double-stuff". The true spaces are separated by red lines: 1-2 is a space, and it is on the same bus "stab" (actually bar) as 17-18.... 3-4 and 19-20 share a stab... 5-6 and 21-22 share... Etc.
And FPE uses the same "straddle spaces with a 2-pole double-stuff" arrangement as GE does on their Qline panels.
That will be important because of "stab limits" -- you must consider the four (4) breakers that you will be sharing the "stab" (bar) with. Keep that number sensible - e.g. 100A. For instance position the 60A breaker so the breakers on the other 3 corners of the "stab" will be 15A. That will put you at 105A, which is as good as you can do. DON'T put the 60 where it shares a stab/bar with a 40, 30, and 15... That would be 145A, bad idea.
Beware of Multi-Wire Branch Circuits (MWBC)
This house seems to have many multi-wire branch circuits where 2 hots share a neutral. It is absolutely vital these be positioned correctly. Specifically, they must be right next to each other, and straddling two spaces - they must be on opposite poles, and there must be 240V between the two hots. And the handles should be tied, but good luck finding a handle tie for a Stab-Lok!
So for each 120V circuit you are thinking of moving, follow the hot back to the cable where it enters the box. Make sure the hot, neutral and ground are the only wires in the cable. If it's not that way, don't move it!
Move two 120V breakers to the 2 free spaces at the bottom
So, with all that in mind, you can identify some 120V-only (not MWBC) breakers fit for moving to the 2 free spaces at the very bottom. (1 and 17). Choose breakers so the hole you are leaving straddles a red line.
Then you can just drop a 60A double-stuff 2-pole FPE breaker (if that exists?) into the empty space.