The two screw holds at either end are two far apart from the mounting holes on the back of the tv. Can I put the screws through the other gaps?
Yes. You'll need decent washers though unless you want the TV falling off the wall.
First off I'd check how secure the bracket is on the wall. Grab the top of the bracket and try and lift your feet off the floor - it should take your weight easily. If it doesn't, then obviously don't put the TV on there! It looks like they've used fairly big coach/anchor bolts. Are there washers on them? It doesn't look like it from the picture. Personally I would use washers on there to stop the risk of the whole bracket coming off the wall. If it's secure enough without them though, don't unscrew the bolts because anchor bolts are only really good for one off use. They don't re-tighten so well (plus the block wall they're screwed into might be cracked if they've been overtightened).
To fit the arms it's easiest if you lay the TV flat on it's screen. I used to put my sofa cushions on the floor and rest it on them, keeping the pressure on the casing of the TV rather than the screen. Then lay the arms on the back of the TV, line up the holes and screw them on. Do them finger tight first, then tighten with a spanner. You want them about a 1/4 turn past tight. Don't overtighten otherwise the threads could crack. You can screw the arms on in different places to adjust the height of the TV on the wall.
The whole lot should either slot back on to the bracket or you may have to slide it on from the side.
Can you tell from all that that I was paranoid as fuck when a hung my TV on the wall?
