Valkyrion

He can use as many per phase as are appropriate. I don't mean that to sound deliberately awkward, but he can use any 'Instead of making a Shooting attack' powers as often as he could normally make shooting attacks (usually 1), plus whatever others are allowed in other phases.
 
So in one full Thousand Sons turn he could theoretically use -
Telekine Dome (instead of moving)
Telepathic Fugue (start of any phase)
Divinatory Aegis/Biomantic Augmentation/Pyromantic Combustion/Thaumaturgic Succour (instead of shooting)
Pyromantic Desolation (in addition to attacking normally)
Biomancer's Rage/Force (psychic weapon in the melee phase).
 
Other rules interactions prevent this specific set of powers being allowed. 
 
In the opponents turn he could use any ranged Psychic Weapon to Return Fire or Overwatch (but not a Psychic Power that is used in lieu of making shooting attacks) and both Pyromantic Desolation and Biomancer's Rage/Force  in the opponents melee phase. 
 
I think. That's how I've played against it (only once, mind) and my reading of the rules confirms this, but to be honest the simplicity of this editions psychic powers is weirdly confusing because I keep expecting to find a 'aha! gotcha!' rule somewhere.

The answer is - it depends...
When you buy a multipart kit, there are usually 2-4 leg parts (left and right, and sometimes the shins), and 2 torso parts, and those are all designed to go together. Lets call this Body A.
Then you have a right arm, left arm and gun set up. Lets call this Gun A.
All Body A parts have to be together, and all Gun A parts must be together, but Body A does not always need to be assembled with Gun A.  Sometimes it will look odd with the wrong pairing, but usually Body A could go with gun E, and gun C could go with body D.
So, if you've got the Indomitus Assault Squad you could buy an Intercessor Squad and put Intercessor Gun A on an Assault Marine to make it look like a running Intercessor, or you could put the assault marine weapons on an intercessor and make it look like a standing assault intercessor no problem.  I haven't tried, but you'd probably struggle mixing the Gravis stuff with non Gravis stuff, but could probably make Inceptors with Multi Meltas if you were so inclined.
 
This is how GW have done the HH mkVI tacticals, Intercessors and probably dozens of others - there are only 5 bodies, and 5 gun arm combinations, so technically there are are (5*5) 25 possible combinations from any one sprue of 5, but a squad of 20 repeats very quickly!
 
But don't forget that it's only plastic, so if there's a connector nubbin in the way, just knife it off and glue over it and it will hold just fine. 

I'd hold off if I were you. 
If you're new to the game then you might find it frustrating when something you've recently learned and committed to memory is superseded by a similar but different rule.
 
If you are interested in the lore and art then go for it, but I wouldn't give the rules any more than a passing glance. 
 
Normally, faction rules are only superseded by a new codex coming out, but in the case of 10th edition every faction will be given free rules immediately. 
 
Just a quick note to say I noticed your Raven Guard avatar and name - your codex supplement is from last edition, so it will be even more jarring trying to learn 8th edition made rules for 9th edition when 10th edition is around the corner.  However, it is a nice little Raven Guard centric tome and has information on company composition and suchlike, so if you're a fan I say buy it. 
 

Daemon saves are not invulnerable saves, so no. 

Look at the paragraph above - LA:S can replace Heavy Bolters with Dragon's Breath Heavy Flamers or Twin Linked Heavy Bolters with Twin Linked Dragon Breath Heavy Flamers.
It's a circuitous route, but most options that allow you take Heavy Flamers also allow you take Heavy Bolters, so you could swap the Twin Linked Heavy Flamer for a Twin Linked Bolter to then replace that with a Twin Linked Dragons Breath Heavy Flamer.
e.g - Proteus Explorator - its 20 points for adding twin linked heavy flamer, but only 5 points for adding twin linked heavy bolter, so add the heavy bolters and use the LA:S rule to get even better heavy flamers for 15 points cheaper!
I'd also argue anyway, probably incorrectly, that a TWIN LINKED X WEAPON doesn't actually exist, rather it's a weapon with the Twin Linked Type, just like Shred or Gets Hot. 
If you look at the Armoury, no weapons are called Twin Linked. 
If the rules said something like - all FLAME weapons get Shred, then you'd not argue that a Twin Linked Heavy Flamer wasn't a flame weapon.