I (28m) don’t trust my gf (28f)

This is quite a long one. I’ve been in a relationship with my girlfriend for one year. I love her and it’s been a good relationship with its ups and downs. Despite this I still don’t feel like I trust her. Here are the scenarios in which made me question my trust in her…
My job involves working in the merchant navy as a cadet from the UK. I spend a lot of time at sea 4 months on. During a trip when I had arrived in Korea, my first trip with the job. I contacted her and she was out partying and taking cocaine with a random dude I didn’t know. I expressed my paranoia with this situation and she quickly told me that I was overthinking. She spend two days at this guys house as apparently “he had free drugs” and she was too tired to make her way home. I told her I thought this was weird she was spending time with a random guy I didn’t know. I then FaceTimed her and she was acting a little shady, she left the room was speaking to me in the kitchen whilst the other guy was in the room sleeping with a prostitute she told me.
She told me she was just lounging on his couch while he got off with a prostitute. I immediately felt sick thinking about the situation. She then made her way home and apologised to me saying it was wrong and told me that nothing had happened and that she understands why it would make me uncomfortable. I decided to forgive and forget in a bid to exercise trust.
The second scenario. So a few weeks into my deployment I have barely any internet onboard and was sailing through the pacific. I contacted her on a weekend to catch up, she was on a night out and I knew this. She was with her friend who I knew and everything was fine. It wasn’t until the next morning (her morning) due to time differences that I’d realised she was still out. I asked her where she was and she told me she was in the southside of the city at her friends apartment (friend of her friend). I grew suspicious as she wasn’t contacting much. I decided to check her location on findmy iPhone (she had previously set up location settings on both our phones early into our relationship). Which I was ok with. But I decided to check this to see if she was where she said she was..I soon realised she was nowhere near the southside of the city and was in fact up on the north side according to the findmy map.
I immediately messaged her as normal and reiterated the point saying “how is the party?” “Are you close to home?” To which she repeated she was in the southside at her friends apartment. According to google the street is houses, not apartments (or flats as we call them in the UK). Big difference. It also had a garage so you wouldn’t classify this as an apartment or “flat”. I then outed her for lying about where she was and she responded saying she never knew where she was as she was drunk and got into the taxi. I call ******** as we are from a small city and she knows fine well where she is at all times. She is smart and calculated. Doesn’t get drunk to the point of forgetting where she is. I then phoned her (no answer). Tried again and she answered from another room. I could then hear a ton of guys in the background and asked her who was there and instead of saying it was her and her friend’s friend. She listed off a bunch of guys I’d never heard of. At this point I knew she was trickling the truth and forever keeps information from me.
Later when I had got home everything was forgotten about and it was fine. It wasn’t until one day I was trying to remove a virus from her laptop I noticed her Facebook logged on. I decided to read her archived messages (not proud of it). One archive was from her friend talking about that night with the guy taking cocaine. The first scenario.. it was from these messages I realised she had slept with the guy before. Which she kept from me. One message read from her friend “I wonder if he wants you to join in with the prostitute” to which she relied “hahaha he lucky I was speaking to my BF at the time” when I had phoned her to find out who she was with. Also in the messages she had mentioned to her friend she had snooped his phone while he was sleeping with the prostitute and found out the guy had a threesome and told her friend “I am glad I never put out to the guy” then made a joke that if the prostitute is getting paid then maybe she could of got paid as she “slept with him for free”.