Fun questions... I don't know what kind of answers you are looking for, but I will give you my views, I understand that I have had experiences with extraterrestrials, and from my experience and understanding of the species I can for the large part only share my interpretations from the experiences, which means they are opinions/assumptions based on my understanding and probably not entirely true (while I may also add more objective perspectives based on what I know as a human) - though I don't imagine you're looking for anything else as there's little scientific facts related to their existence. I rarely make posts based on individual interpretations etc. because I don't think it leads to anything more than speculative and potentially interesting theories, but in this case I will.
1. With our current understanding of physics time travel seems like a very possible scenario. Can these civilizations capable of interstellar travel use time travel?
I am not sure. The species I have had encounters with have been capable of teleportation. I imagine this is some conscious "information exchange" which passes the 'barrier of light' - making time travel very possible (time as we know it is bound in light). Based on other connections I also assume time travel is possible. I think some beings do this without the use of machinery though, and more-so based in their own "awareness", much like how we move an object with our arms...
2. Can aliens love humans in platonic and romantic senses?
Good question. I am sure there are alien species that can and do love in a platonic sense, I am not sure about romanticism.
Remembering "love" as a concept, the connection(s) implied behind the word is/are loosely understood.
I translate my understanding of "love" to "respect" as this gives a more grounded perspective on "love" which is instead understood through the regard of other life.
I know that there are extraterrestrials that act with respect towards humans and I suppose also other life forms around the universe, this could be translated as love, as a feeling or consideration.
It's also a logical conclusion, that if there are intelligent beings of biological origins they probably have an emotional connection (based on our understanding of physics) because emotions function much like a 'instinctive command centre', I think it's important to have emotions for lifeforms (as I understand them), so the interaction of "hate" and "love" are made very probable depending on the perspective/understanding of the being.
As for loving romantically, there have been interpretations made from the Egyptian times where extraterrestrials had sex with the local people, but I have no personal understanding of this.
I think it possible for same reasons as above.
Mainly, the rest of your questions require a large amount of speculation. As per forms of entertainment/music - it's probable. If we use ourselves to relate to the universe and other potential lifeforms, we can imagine there are others with the intention to express their emotional and scientific connections which may result in arts, music, dance etc.
With regard to religion I would doubt that any highly intelligent species have a "religion" as such because a religion is more an interpreted story than a meaning for life, and I imagine that a species that has a good grip on science and self evolution wouldn't follow rules based on something non-factual, as that would restrict individual development.
We know relatively "little" about the universe and probably always will; the more we see through our scope the more of the image we realise there is to discover (all the 'missing pieces' reveal themselves), it's not definite that this process will continue for infinity, but it seems logical, and I would like to think so...
Hope you don't feel you've wasted your time and that I might have offered something you were looking for.