I don't see any great issue with any of this, either. I would also say that three auditions in six months is not a great hit rate, but you'd be surprised: it's better than some actors do in a year! Don't be misled by those who claim to be submitted for something twice a week - it may be the case that their agency is genuinely top notch, or it may be the case that they are remarkably saleable, and there are, of course, those actors who spend all year going to auditions and never land any, and those whose auditions are few and far between but land everything they are put up for. As has already been said (very wisely, I think) the comparison game is pointless, because there are 100 reasons why you are generating less (apparent) interest than others, and it may be a combination of look, skills base, accent, age, experience and many, many other things that you have little to no control over. Interestingly, if you know that others *in your agency* get to attend far more auditions than you do, it may, ironically, be a positive sign, inasmuch as you know that your agent is at least proactive in getting clients seen. If it appears that they are unable to sell you specifically, of course, then that may well be enough to encourage you to look elsewhere for a different representative, who may understand your gifts better, or have better contacts in fields you are actually suited to work in.
In this specific case, however, the reason the agency appears 'dodgy' is because of those two central elements - the need to get you to sign a formal, and binding, contract, and the desire to have you pay to be placed on the website. These are two telltale signs of the 'cowboy' agency, which exists to make money out of you at your expense. Because of this, rest assured, their own reputation will not be good with the majority of industry professionals who may be aware of them, and they would be hard pressed to make a contract that you have not signed (and which is rooted in questionable tenets in the first instance) stand up if you challenged it with, say, Equity's backing. Be as polite as you can; keep a copy of the email you send, any replies, a copy of the contract etc. just in case of any comeback, and leave with impunity. I very much doubt such an organisation would dare to 'follow up' because they know that none of their own practices bear investigation, and they wouldn't want to be put out of business!
For future reference (and because we all learn from bad experiences with agents), it is worth asking about contractual obligation and upfront fees at initial interview before you sign with the agency. The valid agencies out there tend to operate, in fact, on the basis of 'probationary periods' and 'gentlemen's agreements', informal as that may seem. And you should never get in with anyone who is asking for any form of fee whatsoever.