the person who will be opening your account will be a bank employee. The bank employee will receive a kickback from the agent for opening the account. I suppose that there is always the risk of bank employees stealing funds from bank accounts, no matter which country you are in. Bottom line, if you don't feel safe with this process or are afraid that you may lose 3K THB, then don't do it. Instead, just keep running from bank to bank hoping you might find one sympathetic to your situation. BTW, I used one for the exact same reason 5 years ago. I've had 800K in my account the whole time and so far no problems. I guess you have to decide what level of risk you are willing to take on.
Many people on this forum don't like to use agents, and I understand why. Most of the time an agent is a waste of money because you could do what the agent does all by yourself (e.g. apply for an extension of stay, get a Thai drivers license, etc.) However, when it comes to opening a bank account on a tourist visa, I'd go with an agency every time. It's probably going to cost 3K THB but it's worth every penny IMO. The agent will walk you into the bank and you will walk out with a bank account book in hand. All the BS of running from bank to bank will be finished. One more thing, recommend that you open an account with Bangkok Bank. This will make large money transfers to TL easier, especially if you choose to use Wise, like many of us do.
I've never used them but I've heard good things about Motts Services in Pattaya (I'm pretty sure you can find them on FB.) I just went to the Department of Land Transportation and did it myself. Regardless how you choose to do it, you'll need to be there in person to take the eye exam.
Many drugs are available over the counter here, without a doctor's prescription. Three of the most common chain pharmacies in Thailand that come to mind are Watsons, Boots and Fascino. If I were you, I'd do a little research on the web and see if you can buy your meds while you are here. There's even a chance that they may cost you less money, especially if you are from the US. Cheers!