Answer to: How to fix "slide to power off" screen that randomly shows up?This is probably a problem caused by the water damage that must have come into contact with the water module resulting in these 'glitches'. Also charging your phone while drying the water is very high risked since the electronics should be off so that no extra water damage occurs. Relating to the lock button I would recommend getting it replaced by someone you trust who knows how to fix iPhones or going to the Apple Store but they don't fix devices that have undergone water damage because it voids their warranty.
Answer to: no signal, motherboard or antenna issue?It could be an issue with the SIM card not touching the metal plates on the phone resulting in the no signal issue. However it could be the software could be functioning abnormally so restore the phone. But if none of these work then you could try contacting your phone carrier to see if they blocked you from calling.
Answer to: Can I take the screen out, without turning it off?Yes you can but there is a risk of you hurting yourself (small electric shock) or a greater risk of the phone being damaged with contact of water since the phone is on. Just make sure that the exposed motherboard does not get into contact with anything so that no extra damage is done