From my personal experience, when you first start out it is nearly impossible to avoid the said kind of customers you describe. I was lucky enough to have a mentor who have been in this line for over 20years to guide and advice me and I'm gonna pay it forward today.
You can't control their mentality but you can control yours.
1. ALWAYS presume the customer that approach you are either underplaying the problem (Why? Because it their mind, smaller problem means smaller bills) or they have absolutely no idea what they are talking about besides the obvious ( which is why they need you).
2.Don't be lazy, check everything and check for water damage. Those are the damages that will cost you financially and mentally, stains that are not suppose to be there are not suppose to be there. ( Customers are smart now, they know they could dry out their phones either by hairdryer, rice or silica. They dry it out, use till some obvious problem comes up then approach you about THAT problem, not telling you they drop their phone 1 month ago into water )
3. Always cover your @%^, do not over promise and always be honest. Be honest about what you are going to do, what you can do and what you hope your customers would understand, tell them upfront. ( Most customers who are understanding are honest, and those that are not.....well in my case I would show them the door )
4. Don't abuse trust, simple explanation is "Like attracts Like". You want the honest customers, not the other end of the spectrum. So be the one you like.
5. Don't be afraid to ask questions, it is your domain they are stepping in, your forte, not theirs, they cannot BS you. Alot of time you catch them in their lies. By making them talk alot.
6. If its your mistake, owned it. Because you paid for that mistake, I guarantee you will remember it. Mistakes could be technical or you simply got fooled by a customer.
7. You've only got 2 hands, finished what is at hand ( meaning if you are mid repair, make sure you stop at a comfortable stage where you can easily go back to) Then deal with another customer 1 at a time. Not check 2 phones at the same time explaining multiple types of symptoms to multiple customers. If you try to multitask everything you will most definitely screw up somewhere. It is because you are focus, and that makes it harder for customers to pull a fast one.
These are the few key points I can remember off the top of my head, and there are a lot more which is situational. Good Luck.