Some of those minimum clearances are defined in building codes and will vary from place to place. In Ohio we use the International Plumbing Code (IPC) and it does define some of these minimums and local municipalities might add additional regulations. But it sounds like you may not be as concerned with the minimum specifications, what you really want to know is what "feels comfortable" and looks/feels good. Unfortunately a question like that is tough to answer.
Luckily people have been dealing with small bathrooms for ages so there are a number of strategies you can employ and there are some specialty fixtures that can help, like narrower bathtubs (28” instead of the standard 30”), shallower vanities/sinks, shallower toilets (10” rough-in instead of the standard 12”), etc.
If you can find a copy of the codes your area uses that can be a good resources if you have the patience to read it. I would recommend an electronic version so you can search for terms.
In the IPC the relevant sections I found are here:
Section 417.4 Shower compartments
All shower compartments shall have a minimum of 900 square inches of
interior cross-sectional area. Shower compartments shall not be less
than 30 inches in minimum dimension measured from the finished
interior dimension of the compartment, exclusive of fixture valves,
showerheads, soap dishes, and.safety grab bars or rails.
417.4.2 Access. The shower compartment access and egress opening shall have a minimum clear and unobstructed finished width of 22 inches.
Section 405.3 Setting
405.3.1 Water closets, urinals, lavatories and bidets. A water closet, urinal, lavatory or bidet shall not be set closer than 15 inches from
its center to any side wall, partition, vanity or other obstruction,
or closer than 30 inches center-to-center between adjacent
fixtures. There shall be at least a 21-inch clearance in front of the
water closet, urinal, lavatory or bidet to any wall, fixture or door.
Water closet compartments shall not be less than 30 inches wide and 60
inches deep.
You mentioned that you are retiling and I think your tile extends under so that doesn't matter.
your hot and cold for each sink are already probably close enough or were they need to be. Maybe you have to move them over a foot or two... This is an easy DIY
drain pipes for sink. May have to move these over a little but maybe not. Unless there is something really odd going on in the wall where you can't move a drain over a foot or two, again no big deal and maybe no issue at all. This really depends on what kind of cabinet you get and if it has drawers that would get in the way.
Know that your plumbing can be anywhere really. Need to just make sure your cabinet if functional and plumbing meets code - for instance you can have your hot/cold shutoff in the corner of the cabinet if it fits there.
Also if you do have to change these things your wall doesn't have to look perfect after with a cabinet going over. Throw up some drywall and a bad mud job.
Maybe you get taller cabinets for the modern look? So what you have to think about is the mirror has to go up and then possibly the vanity light. Still moving this is taking out a couple of very small squares of drywall.
How much space from tub? Doesn't matter as long as it doesn't create a safety factor. I personally would make it none or a lot (at least a foot). Very weird having 3-4 inches to clean there.
And my take as a cheap flipper... Tile has to go. Cabinets aren't bad and mirror looks nice. Paint the cabinets - maybe they need new doors. So I might order new doors. The counter goes. I cut out the middle section. I throw on granite on each cabinet, install undermount sink, and backsplash. Right under 1K. Can usually pick up granite and undermount sinks on craigslist as leftover or overstocks. Your 49" is an easy find. 53" a little harder but they are there too.
Best Answer
This is the best I could come up with your criteria. I like your design much better.
My drawing is very roughly to scale- I didn't spend too much time- I just wanted to see if there was a way to fit all that in there.
Trying to get that window to be in the hall bath just wastes too much space- basically creating a hallway.