Hi,
I'm no window fitting expert but I have fitted a couple in my time and your fixings up the side & bottom look fine. I would use 1 top fixing on a window of that size, I would put it in the middle. Some will say it's not necessary or shouldn't be fixed at the top but it stops the head from dipping down in the middle, this is more of a problem on a wide frame, so it's up to you if you use any fixings in the top.
If you do and the lintel above is steel you can use a baypole screw, this is a threaded screw with a tip like a drill bit, this will drill into the lintel and then screw into it, ask at any window fitting place and they will probably give you a couple.
I would screw the frame to the cill before fitting and fit it as one unit.
Put a thin bead of silicone along the back edge of the cill where the frame sits, also put a very thin film along the front edge, (Red Dots on photo) wipe any excess that squeezes out off. Make sure you only put a tiny amount along the front edge, just wipe it on with your finger nice and thin !
This "wipe" of silicone along the front will stop any wind driven rain getting through into the void between the frame and the cill.
Also fill the voids between the frame & cill at the ends (Green on the photo)
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With the frame screwed to the cill offer the frame into position, space it up about 5mm from the brickwork with plastic frame packers, this should give you a 5mm clearance at the top if the window is the correct size. If not adjust the frame up / down with the packers until the clearances are equal, do this for the sides also, don't forget to check that the window is level across the bottom & plumb up the sides and set back into the brick work equally on both sides.
Put plastic frame packers between the frame & the brickwork wherever you have a fixing so that when you tighten the fixing it doesn't distort the frame.
I would use frame fixings not hammer fixings (maybe this is what you meant) so if you need to you can loosen them off again so you can adjust any packing you have behind them.
Not 100 % necessary but once fitted & fixed you can use expanding foam around the frame, this is best done with a foam gun as you can control these very precisely unlike the hand held cans. If you do decide to use a can put masking tape around the frame so if the foam goes wild it won't stick to the frame. If the foam comes out of the gap between the frame & the brick work it will have to be cut back slightly lower than the frame before any silicone frame sealant is used.
When fitting the glass panels, try the panel in, you will have to place it on plastic packers that normally come with the frame, you place these at the bottom of the glass about 6 inches in from each corner (this measurement isn't crucial), these packers are to lift the glass panel so that it has the same clearance top & bottom in the frame, this is so it looks correct when the beads are fitted and the distance from the edge of the bead to the silver spacer bar in the glass panel are equal. Move the panel from side to side to equal the gap also.
When the bottom panel is centralised place plastic spacers on top of the panel in the middle, this is to hold the crossbar (transom) of the window level and to stop it drooping down, this is important on wider frames so may not be required.
Fitting the beads that hold the glass in place can be tricky, you shouldn't have any problems with the bigger panel, but on the smaller panel make sure to fit the smaller side beads first, then bend the bigger ones & fit the corners then tap it into place with a rubber mallet, you will get a satisfying crack when it jumps into place, if you are having trouble fitting them apply some silicone spray to them to make them slide into place more easily.
Hope this helps you.
Good luck.
Cheers.