I hear "ca y ta..." as well. Thanks for putting the course together and/or all the help!
Such final consonants are often just "stops" so you hardly hear them. For example, my girlfriend's first name is Ngọc; that final c sounds more like a "swallowed" b than like a c. So it's quite normal, I think, for the final c of các to sound more like a "cut-off" than like an actual c...
supporting is just a present participle, it needs the presence of the auxiliary be. otherwise your sentence is incomplete without a verb.
Is there a significant difference between "ủng hộ" and "hỗ trợ" here? Are they both used the same way or are there any differences in meaning?
you would use "ủng hộ" more likely but not exclusively for mental or psychological support. eg. a fan cheering on their idol, their favourite sport team; a person/group/party of influence favoring one side over another; people contributing to a charitable cause; etc. synonyms: to support, to back, to cheer on, to encourage
you would use "hổ trợ" for material support. eg. a patron funding artists; a brand sponsoring a star; the army backing up the authorities during natural disasters; etc. synonyms: to support, to help, to give assistance