it is derived from dil (heart), and dar (one who holds) from masdar darad (to hold), hence dildaar is one who is beloved; however, the word has its own meaning, regardless of how and from what it is derived, so from this pov perhaps there won't be any shara'y hukm (of impermissibility) using this word but should be avoided due to having some physical connotation (even if not intended), and other unfavorable meanings.
no, it has several meanings, (i) something/someone that/who gives comfort (tasalli bakhsh, tasalli dainay wala), (ii) beloved, (iii) thick or heavy (if read with zabar on daal, daldaar), only the second meaning is favorable, one would intend to mean that; however, due to having other unfavorable meanings it should be avoided.
I wouldn't use it. We should be careful when selecting words in such cases so it's better to stick to other words.
It means beloved. But is it related to dil (heart)? If so, is it appropriate to describe RasulAllah ﷺ as the dildar of Allah?