The initial end is bonded to a "support" (glass beads called cpg are typical) and only cleaved from the support once the entire chain is grown. The cleaving process also caps this end.

Good question - one reason is that the chain isn't flexible enough to make such a tight turn. Still, a free nucleotide building block could hydrogen bond to a growing chain. But that would only be 2 or 3 H bonds, and thus much too weak to stabilize the complex

The “cap” only allows 3’ additions OP probably simplified the wording it’s not an actual 5’ cap (as you hear about in mRNA), it’s a chemical blocking done by modifying the 3’ end of the chain. The 5’ is never exposed.