I think the really important aspect of the relationship for you is having the ability to feel that you can communicate with your agent, that your wishes and interests are being listened to, that you could arrange a personal meeting to discuss the direction your career is being steered in without fear of being fobbed off and so on. All these things need to be in place in a good actor-agent relationship and if you feel that you cannot hold your agent accoutable to you in some way, then this is a bad business partnership!
With that said,whether or not providing the client with breakdowns for work that they have been put forward for but didn't get is really the agent's personal prerogative: some are quite happy to do it on request (as my agent is), whilst others are very reticent - but you can understand why they say they will let you know only when companies 'bite'. Its a simple way of maximising their time usage; the important information that needs to be channelled to you directly is the information about the auditions you have been specifically requested to attend. It can be reassuring to see a list of what you have been put up for, just to prove to yourself that your agent is working hard for you, and very often this list can also show you what casting bracket the agent feels you are in. But, in of itself, its rarely information that is useful to further your career - you hope to see the applications mainly to reassure yourself. With that said, it is not hard, now that most applications are made via the Spotlight link, for an agent to simply cut and paste the most recent applications on your behalf and send you the links by mail if they can be prevailed on to do so. If they are logged in, and you can see *their* computer terminal, they can also show you this information direct from their Spotlight account. Neither method necessitates endles man hours spent compiling lists on your behalf. What may be happening is that there is no easy way to give you the information you are looking for over the phone; instead, seeing if you can arrange an email attachment or, better yet, a personal meeting with a chance to look at recent applications may be a better option.
Tattoo - wise, I'd say that is ultimately a decision that is up to you, but, almost certainly, any tatoo on any area of your body which is likely to be exposed regularly in, say, standard summer clothing may well be an inconvienience (i.e. anywhere near the neck line, on the shoulders, arms,lower leg, middle of the back). You may get away with more intimate tattoos elsewhere for the most part. There is always the option for make-up artists to blot out tattoos anyway, but its always more work, and, if your casting range is typically comedy, say, then simply having a visible tatoo may work against your casting bracket, and you are less likely to be seen as 'funny' or 'approachable' (unless that's what you were hoping for ?). I would hope an agent should at least be able to advise you on whether they would condone you having a tatoo or not - I wouldn't expect them to tell you exactly which part of the body they'd allow you to have it on - if they will allow it, I'd just apply common sense here.