Air carrier Captain reported the ramp had non-standard parking markings and had no tug or tow capabilities due to the lack of wingtip clearance for larger aircraft.

Narrative

PM marshalled in to ramp. Yellow lines on ramp were completely disregarded by ground crew. The yellow parking markings are completely non-standard and look like a squiggly maze. And solid lines intersect dashed lines in a curvilinear pattern. We were parked well in front of any yellow line. We assumed we would be pushed back. From the cockpit it looked way too close to taxi forward and make a turn. I was in fear of hitting the terminal with the winglets. I expressed my misgivings to the person in charge of the marshalling and he proceeded to argue with me and told me he was responsible for the aircraft when parking. I politely informed him that as the Captain I am responsible for the aircraft in its entirety. I took many pictures and videos of the proximity of the aircraft to the terminal. The ground operations personnel measured the distances and I relayed their information to Flight Operations. Spoke with Chief Pilot and another Captain to try and figure out solution - all were extremely helpful and supportive of my decision not to attempt to taxi aircraft out. There was no tug that was rated for our aircraft and no tow bar.Cause: Lack of clearly communicated expectations. Lack of standard parking markings. Lack of appropriate ground equipment. Lack of training of ground crews. Poor communication. Lack of information in the company airport pages of Jeppesen App. Lack of understanding on the part of TKPK staff that the Captain is responsible for the aircraft in totality and when he/she briefs a Marshaller; it should be taken completely seriously because aircraft safety is a very serious business. The parking and taxi out procedures are very unique to this airport and I suggest all captains conduct a thorough briefing and assessment with the marshallers prior to departure. Parking procedures and markings should be standardized.Suggestions: Operations needs to send a team to assess the parking lines painted in front of the terminal. The company operations advisory pages need to note that no tug or tow capability exists and not to park where you can't turn out comfortably. And the ground crews need to be trained properly. The airport said they've had problems with our ground crews not following the markings when marshalling and they said the markings were placed there for safety. I told the Marshaller and Airport Management to get together and talk about it. But I must emphasize that I couldn't make heads or tails of the weird parking lines. It was like a dot-to-dot puzzle. The ground crew are also used to different aircraft - but I still would be very uncomfortable parking so close to the terminal. The poor passengers had a terrible time and I feel awful and truly embarrassed about the whole situation. Someone needs to come down here and sort it out. Procedures need to be established; explained; and followed. The large parking area to the right of the terminal also needs to be clearly marked with standard parking lines and there needs to be company notes stating that.There is no tug or capability to push back - again - so don't park where you don't feel comfortable taxiing out. The ramp has a marked downward slope. Do not release the brakes until after engines are started and chocks are removed - or you will get stuck because the aircraft will roll forward onto the chock. Also; the agents at this airport should not line passengers up outside in the heat until the agents are completely ready to board the passengers. We had disabled passengers clearly in heat distress from standing on the ramp waiting for the aircraft to be cleaned. And; the agents do not ask the pilots if they are ready to close - they just stand around until you finally get up out of your seat and tell them to close the door.