The d in codladh and words derived from it is not usually pronounced.
Only one of the 4 or 5 different Munster speakers pronounced the "d" - none of the Connacht or Ulster speakers pronounces the d in any of the examples.
Codlaím would sound more like culeem than cud-leem.
Not in my experience - it's the dl combination that is in question, not whether it's used in a verb or a noun or an adjective, so the d is pronounced in the past tense and the imperative (codail) because the d and l are separate, but in the other tenses, the d and l come together, and the d is not generally pronounced. (Wiktionary specifically mentions this).
As for codlata (not codalta), the two examples on teanglann show that the Connacht and Ulster speakers do not pronounce the d, but there are mixed results from the Munster speakers, and, stranger still, the speaker who pronounced the d in codlata didn't pronounce the d in codlatach.
And, of course, there are the exercises that pronounce codlaíonn here on Duolingo, by a native Connacht speaker.
Codlaíonn an buachaill eadrainn gach oíche
Codlaíonn na madraí sa chiseán
Codlaíonn mo chat ar a leaba
Codlaíonn na daoine óga ar maidin
She also pronounces codlaím in this exercise, and a number of others.