1. Depends on the tires and the max weight capacity of the tires and the trailer. Read the specs on the tires and see what the max load and max psi is. Generally inflating them to the max is too hard for normal use, and the trailer will be bouncing around all the time, but if you're close to the max weight capacity of the trailer, you might need to inflate the tires a good bit for them to handle the weight. the 12 inch tires on the trailer I have say they are rated for 990 lbs each, and max pressure is 90 psi. I keep them at 50-60 psi for normal use, but if I were carrying 1500-1600 lbs of motorcycles, I'd probably up it to 70 psi or maybe even 80. A good way to find out what works is to eyeball the tires with the load in the trailer and hooked up, and make sure first of all that the tires aren't too compressed. The bottom on radial tires should look a little bulged when loaded (by design), but not extremely so. You can also just inflate the tires to 70-80 lbs and then let some air out when towing if the trailer seems too bouncy. Also keep in mind, it's better to have too much air in the tires, even if that causes a bouncy trailer, rather than too little. Underinflated tires that don't have enough pressure to handle the load can overheat and blow out. Usually the worst that happens with tires that have more pressure than they need (but aren't overinflated past their max psi) is they give a bouncy, rough ride and might wear in the middle of the tread and not evenly.
2. Depends on the tires, but not really. If you have P-rated tires with a max psi of 35, you might want to either be sure they are inflated to the correct pressure, or add a psi or two in the rear for towing. If you're going to be towing all-highway for a long trip, you might even just bump up the pressure on all 4 tires a psi or two, to get better mileage. Don't forget to check the spare tire pressure as well while you're at it.
If you have LT-rated tires, which usually have a max psi rating of 44 or 50, you probably don't need to inflate them over the proper psi for the vehicle, but again, you can always add a few psi to either the rear, or all 4 tires for a highway trip.
Finding the 'right' psi for trailer tires, or even for your vehicle tires, is usually a long term thing you have to discover by experimenting, but when doing so on the road, or a trip, it's usually easier to start by inflating the tires to the higher psi, then taking out some pressure if they feel too rough or firm, rather than starting out soft or at the low psi, then having to bust out the portable compressor and inflate tires while they are hot.
