Carboy/Secondary Questions

I have three questions. Hopefully they are easy. Thanks in advance for any input.
Q1: Can I use a 5gal Carboy as a primary fermentor or is there not enough space to ferment a 5 gal batch?
Q2: I f there is not enough space can I short the batch 1/2 gal and add the other 1/2 gal when I go to the secondary?
Q3: Should I rack to the secondary or should I pour and strain?

1. There isn't enough headroom in a 5 gal carboy for fermentation of 5 gal. You'll lose a lot of active yeast and head-retaining protein out the blowoff tube. It's possible I suppose but not ideal.

2. I haven't had experience adding water after the fermentation. I don't see that it would be too much different from topping up to volume after the boil as long as it's boiled and cooled. That's probably the biggest problem - infection possibilities.

3. When transferring to secondary never pour. You want to have as little contact with air as possible to prevent oxidation. Many people purge their secondary with CO2 to minimize this even more than just racking.

Edit: If you want to strain when racking to secondary, you can use a vinyl mesh bag on the end of the hose, just keep it all submerged to reduce oxygenation.

One follow up question?
Is it a good idea to strain the wort into the primary or is there an advantage to increased trub in the primary?

I wouldn't say there's an advantage, but there's not a whole hell of a lot of disadvantage. This has been discussed elsewhere in the forum and I think they determined no adverse effects to the beer. The only real problem with more trub is more that you leave in the fermenter. Leaving it in primary long enough compacts it pretty well though. I've always poured through a mesh bag to strain out the hops and some hot/cold break. I'm now thinking I don't know how much all the extra material in the wort would change a OG reading.