There has been a lot of disc-cussion (disc - get it?? hehe) about this.
Some people say if you mount it flat there is more risk the heads will hit the platters causing a fatal crash where as if you mount it on it's side then you only get disc read/write errors as the head moves.
other people say mountig it flat is fine as this is the way HDDs are supposed to be.
one important thing though is to only mount it flat or on it's side as any angle inbetween is really not recommended byt he manufacturers.
I would do a on things such as HDD failure and mounting and see what conditions people have had drives fail under. To be honest i would get a new drive with a 3yr warranty and mount it flat and keep it backed up. that way you wont get annoying errors requiring fixing and if it does have a major crash then send it back
as for mounting next to the PSU a lot of people so this. at the end of the day your PC parts are pretty close tghter in your home PC. I would give it a bit of room though from the inverter and PSU if you can just to be ont he safe side but most HDD are well shielded these days. I would be more worried about the ribbon cables and any strong magnets - eg speakers, motors - oh and the transformers in your inverter and coils in your PSU so maybe leave abit of a gap. But nothing huge.
Normally, outside of a car it shouldn't really matter which way a hard drive is mounted because the heads sit on a cusion of air as it is in use rather than anything based on gravity. They do get used to being in a certain orientation though due to the cumulative effect of gravity on certain parts so with old drives that have been in one orientation you can find they are only readable when positioned that way.
In a car all the strongest shocks are verticle as you go over bumps, turning is nothing in comparison, and you want to mount the drive vertically because the heads are freely floating above and below the disc and any shock will cause them to move in that axis, possibly into the platter. Not only will the mechanism holding the head in a certain position on the platter give much more resistance to the shock than the air cusion but as mentioned before if a shock is big enough it will only cause a read error.
Laptop drives are much more resiliant than standard drives. Because they are smaller and because they are specifically engineered to deal with a certain amount of shock while in use. Also they are better for power and heat reasons.