Help Is it possible that one apps get the data from another apps?

The data you are talking about (images) are not tied to any app. They are stored in the SD card, and any app that has the permission to read the SD card can access these files.

Accounts are stored in another area (I don't know exactly where). All apps, have access to view available accounts. (Goto Settings >> Accounts to manage them...

But yeah, sometimes apps can share some data of their own, this can be chosen by the developer.

To disallow apps from taking such data, you will probably have to deny the permissions when it asks you for them the first time you use it.

To answer your third question, it really depends on what apps they are and whether the developer wanted that to happen...

The first question is whether the data really are irrelevant. If so my instinct is to avoid the app, but it may be that you've not understood why the access is needed. It's hard to discuss without some concrete examples, and I don't know what your concerns are, but to pick some examples a music player may want access to "telephone", not so that it can make calls but so that it can tell when you are making/receiving a call and pause playing. But it shouldn't need access to your contacts, so I'd be suspicious if it asked.

Denying permissions before installation isn't possible, unless you can decompile and hack the app. What happens after installation depends on the android version. With recent versions you are asked to grant or deny privileges when the app first tries to use them. With older versions you had no say, so you needed to check them and decide whether you wanted to install it or not. Many app developers try to recreate the old days by simply requesting all privileges the first time you run the app and refusing to run if you don't grant them all, even if some were for functions you'd never use, in which case it's your choice whether to grant them or uninstall.

The last scenario shouldn't happen like that. Just because you use the same email address in 2 separate apps doesn't give either of them access to the other's data. Of course if you give both access to your actual emails they could work a lot out, but that is different. An app cannot access another app's internal data (without system privileges, which user-installed apps can't have unless you root the phone). But if the app had the privilege to access "accounts" on the phone it may be able to work out what accounts you have (of those listed in your "accounts" settings).

Bottom line: if you are not comfortable with a particular app having a particular privilege, don't install it. But sometimes there are legitimate reasons for this that aren't obvious.

Applications can detect multiple logins from the same user in various ways. For example, IP addresses and MAC addresses can be used. If multiple devices are on the same Wifi network, chances are they all have the same static IP address, as presented to the outside world.
Having said that, your login/password information probably isn't even stored on your phone. It will be held in the app provider's back end database.
Even if the sensitive information were stored locally on the phone, then there's no way that another app could access that data. This is strictly prohibited by the Android system.