I think it's possible to pronounce the "l" in certain parts of the English speaking world. Merriam Webster has two alternative ways to pronounce the word both with and without the "l"

The pronunciation of the "l" in "psalm" depends on the dialect and regional variation. In standard English pronunciation, the "l" is typically silent, so it is pronounced as "sahm" (/sɑːm/). However, some regional accents may include the "l" sound. Ultimately, both pronunciations are widely accepted, so you can choose the one that feels most natural to you or aligns with the pronunciation in your region.

Yes, in the sense that the tongue does travel to the top of the mouth just as it would with a normal "L". However you do not enunciate the "L" like you would in "lollipop". That movement of the tongue has a big effect on the sound of the word.

both are acceptable 1. sälm, ˈ 2. sȯm,

It varies. I would say that in words like "psalm," "balm," "calm," "palm," you should not hear the L as a consonant. In contrast, in "almost," "salmonella," "ophthalmic," you do hear it as a consonant. The "L" after the "A" indicates a deeper, darker vowel sound, similar to the vowel sound in "cot," "watt," and "sock." These words could have been spelled with an H instead of an L--"sahm," "bahm," "cahm," "pahm,"--but the fact is they are spelled with an L.