I'll first respond to closetnoc's response. The reason you hand over your account to an agency is because you either don't want to or don't have the expertise to do it yourself. This is no different than hiring someone to do other parts of the business such as accounting although I agree it can be scary for some to put trust in someone to basically look after your money. But I agree with you that you should be proactive with your account manager. Also, as far as Adwords is concerned, also agree with your, don't give direct access to the account. A professional agency has a special account called a MCC that can link to client accounts. No need to give email and password and you can revoke access at any time.
To answer the specific questions:
Always use your own account and provide access so they can do their job. The reason is that your advertising is yours and if the person or agency uses their own account, if you want to not use them for any reason later, you don't lose all that was done. If you use your own account, you don't have to start from scratch if there's a problem. You also can see for yourself what they do and the changes they apply. An account manager should be transparent and that's impossible if you can't even access the account from which you are advertising your own business.
In my experience, clients don't really care for the most part about reports. If I created some fancy report with charts and graphs, these would go un-read.
Myself, I keep it simple and say for the last reporting period what changed compared to the previous period. Usually, this is just 2-4 paragraphs. Clients just want to know if there's been improvements (was there more traffic? more sales?), why this happened, any major changes, recommendations and what is being planned.
Reporting just the numbers that can be seen by yourself in your account is useless in my opinion. It needs to be put in context. That's why for most clients I say the CTR increased/decreased and the conversions. I may provide more insight that I've found (new competitor for example). One client used to want me to provide a spreadsheet and calculate revenues based on his average sale. I told him Adwords has such a feature and more accurate.
I can create an account for you. I'll ask you what email you want to use and I'll use a password which I would then forward to you so you have access. But I prefer the client do this himself because Google is going to ask information that I may not know (address info and specifically credit card info). So it would be easier and faster for you to create it. Typically for me, that's not a problem since clients already have an account, I just need access through my MCC and I simply need the account ID, put in link request that the client has to approve.
You could link it yourself, simple thing really. But if you want the agency to have access to Analytics, there's no MCC type of setup for Analytics as there is for Adwords, at least as far as I know. So you need to give access to Analytics separately. It will be the same email and password as all Google accounts, including gmail by the way. You need to trust the agency to go into only the accounts they need to do their job. Most will as they won't have time to peek into your gmail.
But to be on safe side, use a new account. Create a gmail account such as firstname.lastname@example.org which will be used for Adwords and Analytics.
The MCC by the way really simplifies things for your account manager, that's why it exists. For them, they need only one login - no need to switch back and forth among all the accounts they may be managing - and all their reports can be applied to all. It would be a pain to recreate all my reports that I use for each new account. If an agency doesn't use an MCC, they are not really professional in my opinion.