Usually these services have provided BBCODEs in the past. Now they make it hard to find the link to force you to use their embed code which lets them collect data and prevents hotlinking.
Not at the moment. Based on results returned by Reddit's search engine, I see that people are using at least half a dozen different types of URLs. Half of those (seem to) point to images directly that could be used with a [IMG] tag, the rest would need some processing to determine how to handle them. I see three different types of identifiers (numerical, short alphanumerical, and long alphanumerical) and I'd need to figure out what's going on. Tenor has an oEmbed endpoint but it does not support every type of URLs being shared by users.