Should I pre-drill before nailing or not?
Unfortunately the answer to this is, it depends.
With certain woods, particularly when nailing near the ends of boards, pre-drilling can be advisable. A different fix when nailing near the end of a board is to leave the board over-long (where possible) and then cut to length after the nails have been driven home. This is often done on decking boards.
When nailing along the length of a board another way to lessen the tendency towards splitting is to stagger nail positions so that you're not driving the nails in aligned with the grain:
In case you're unaware, the type of nail matters here. Nails with blunt tips, perhaps counter-intuitively, split wood less than sharp nails because they crush wood fibres as they go in rather than parting the wood ahead of them (working like a wedge). And oval nails are better than round nails as long as the long axis is oriented correctly, in line with the grain.
Where the nails you're using are sharp and you'd like to take advantage of the effect of a blunt tip a very old tip is to put the head of the nail on a hard surface and tap the tip with the hammer to blunt it, but it's very easy with soft wire nails for this blunting blow to bend the nail slightly. So it's much more reliable to snip the tip off the nail with side snips or pliers. Nails are commonly only mild steel wire and even with a beefy nail this isn't too difficult to do.
But, it may be disadvantageous because it may reduce the power to grip the nails, making them loose.
If the hole is drilled full size that will occur. The drilled hole should be undersized, roughly 75% of the diameter of the nail.