Arnauti: looks like = resembles = looks like. There may be a distinction in the Swedish (between ser ut som and liknar) but there is none in the meaning of the English terms you mention. E.g. Cambridge Dictionary: "resemble (verb) = look like or be like (someone or something)".
There is a difference, though - for instance, if someone sees you and your father walking, there may be a resemblance in how you both walk, for which you wouldn't use "look like". Hence Cambridge saying "or be like".
This may seem like a silly point, but since the difference is well worth learning in Swedish, we try to preserve it in translation as well. :)
It is necessary.
Ser and ser ut mean different things. Att se (ser) has the same meaning as English to see. Ut changes the meaning of ser, kind of like flipping the direction of the seeing to the outside. Ser ut could be more literally translated to "appears outwardly". The difference between ser and ser ut is like the difference between gives and gives up, e.g. "She gives playing cards" vs "She gives up playing cards".
Ut is an adverb, modifying ser. Som, in turn, is an adverb to ser ut, e.g. "She appears outwardly like a moose".
You can use "ser ut" on its own to mean "look out" in the right context. Han ser ut genom fönstret. He looks out the window. Hon ser ut över havet. She looks out over the ocean. The meanings are pretty different though, so you'll most likely be able to tell which meaning you're looking for just from context.
Generally speaking, behaving like a gris implies being e.g. unkempt or physically dirty, not taking care of their hygiene or not washing their hands before cooking for other people - that sort of thing.
Behaving like a svin, on the other hand, is an issue of moral dirtiness. That middle manager who's sexually harrassing their employees because they know the employees don't dare go to HR and can't quit? Someone breaking up with you over text while also mentioning you'll want to get tested for STDs? Those are definitely swine.
So it is rather like the pig/swine distinction then! If I say "You pig!" what I'm complaining about has more to do with a lack of "personal daintiness" than the moral depravity that would cause me to exclaim "You swine!" Being a pig in English also means going at one's food like a pig at the trough. Would it mean the same thing to say "han äter som en gris"?
Because in Britain, Americas, SA, NZ, AUS etc... we don't normally say "is looking" or "am looking" for something that is constant. "am loving" "am climbing" "am walking" "am surfing" . If you want to say you are a climber, you say "I climb". E.G " I surf" "I hike" "I shoot" mean I am a surfer, I am a hiker and I like to shoot. I am loving is something that is sneaking into English mainly from international users and Indian English. She -is looking- like a moose, is okay, but will mark you out as a non native speaker. "she -looks- like" is much better sounding to natives. Just as we much prefer to hear "She writes, or she is a writer" rather than "she is writing". She is writing is only used when talking about now, or specific occasions, such as she is writing this report (now or currently), She is writing regularly or she is writing 3 times a week.
I disagree with this assessment. In certain communities, this is perfectly acceptable. See e.g. https://www.urbandictionary.com/define.php?term=looking%20like%20a%20whole%20meal
This is not a non-native thing, though it is particularly "slangy."