I'll just fling in things that come to mind on each of your questions.
1. You need to mix reasonably accurately, but with (regular) polyester resins you don't need to be exact. You could pour a measured amount of water into your margarine tub and use that to put a mark on the outside of the tub. Then dry the tub - if you get water anywhere near the resin, it will stop it setting! Popsicle sticks ("non-sterile tongue depressors") are what the pros use to mix!
As soon as you're thoroughly mixed the catalyst into the resin, pour it into a bigger container - more surface area means it won't heat up so fast, so it won't set so quickly. The ideal for this on small jobs is a paint
roller tray - the resin pools in one end and the sloping bit gives you somewhere to put your sticky brush down. Once any unused resin has set, you can bang it out of the tray and re-use it.
2. Number of layers depends on the glass you are using. Around 5 oz/ft2 of glass mat sounds about right - say 3 layers if you're using 1.5 oz/ft2 mat. You can apply this thickness, but not much more, in one work session. Apply each layer individually. Overlap the new glass at least 5cm onto the old glass.
3. Applying by paint
brush is ideal for small jobs like this. Remember that you want to use a 'stippling' (or stabbing) action to wet out the glass - too much brushing risks pulling it all apart. You won't know if a brush falls apart in resin until you try to use it, so a test run first would be a good idea - actually doing a complete test run of the whole process away from your trailer is an even better idea!
Decide whether you will (1) use disposable brushes and throw them away or (2) wash the brushes in expensive solvent (paint thinners will do, but acetone is better) and re-use them - it depends what you pay for brushes and solvent as to which is cheaper. Washing brushes inadequately in expensive solvent and then having to throw them away is the worst option of all, OK? Have spare brushes to hand - you will
get caught out at some point by the resin setting while you're still working with it - stopping work and throwing away unused resin (and the solid brush) is the only solution at this point, you cannot stop the resin setting!
4. Plan A (conventional): Paint resin onto the job, lay a strip of glass onto the resin and stipple it with the brush, so the resin wets through the glass. Add more resin if needed - you're aiming to just wet out the glass, with no dry strands left, but not to add any more resin than is needed to do this. More resin than the minimum needed is not better, it's worse - but it will take practice, so you'll probably put too much resin on to start with.
Plan B: Lightly wet out a strip in the 'dry' end of your roller tray. You've then got about a minute (before the glass mat starts to disintegrate) to lightly coat the job with resin, pick up the soggy glass and stipple it in place.
5. Mistakes can be sawn off or sanded away (wear dust mask for either) - but sanding isn't easy, until you put a sanding disc in your angle grinder (the laminator's friend....). Think again about doing a practice run off the job. You wouldn't recommend anyone to pick up a saw for the first time to trim an expensive bookcase, and fiberglassing is no different.
6. Leave sanding, sawing, drilling until the next day - it can be done sooner, but the fiberglass will not be as hard and will clog tools badly.
7. The only mask that will protect you while laminating (not sanding) is an inorganic vapour mask - anything else, like a dust mask, is completely pointless. Polyester laminators who are not forced to wear masks generally don't wear them. Personally, I use a vapour mask when working indoors, but not outdoors or a garage with the door open. Don't get scared of the materials - for example, polyester resin isn't anything like as dangerous as used engine oil. Don't laminate below 5C/40F. Above 20C/70F, start reducing the proportion of catalyst or the resin will set too quickly to allow you to get the job done.
Them's me random thoughts- I hope it helps, and: Have Fun!