What distinguishes the tests is their respective goal:
* Unit-testing aims at findings those bugs that can be found in isolated small parts of the software. (Note that this does not say you *must* isolate - it only means your focus is on the isolated code. Isolation and mocking often enough are not needed to reach this goal: Think of a call to a `sin` function - you almost never need to mock this, you let your system under test just call the original one.)
* Integration testing aims at findings bugs in the interaction of two or more components, for example mutual misconceptions about an interface. These bugs can not be found in the isolated software: If you test code in isolation, you also write your tests on your (possibly wrong) understanding of the other components.
* Feature tests as you describe them will then have the goal to find further bugs, which the other tests so far could not detect. One example for such a bug could be, that an old version of the feature was integrated (which was correct at that time, but lacked some functionality).
The conclusion, although it may be surprising, is, that it is not in the stricter sense *forbidden* to make data base accesses in unit-testing. Consider the following scenario: You start writing unit-tests and mock the data base accesses. Later, you realize you can be more lazy and just use the data base without mocking - but otherwise leave all the tests as they are. Your tests have not changed, and they will continue finding the bugs in the isolated code as before. They may run a bit slower now, and the setup may be more complex than with the mocked data base. However, the goal of the test suite was the same - with and without mocking the data base.
This scenario simplifies things a bit, because there may be test cases that can only be done with a mock: For example, testing the case that the data base gets corrupted in a specific way and your code handles this properly. With the real data base such test cases may be practically impossible to set up.

Look, there's no easy way to do this. I'm working on a project that is inherently multithreaded. Events come in from the operating system and I have to process them concurrently.
The simplest way to deal with testing complex, multithhreaded application code is this: If its too complex to test, you're doing it wrong. If you have a single instance that has multiple threads acting upon it, and you can't test situations where these threads step all over each other, then your design needs to be redone. Its both as simple and as complex as this.
There are many ways to program for multithreading that avoids threads running through instances at the same time. The simplest is to make all your objects immutable. Of course, that's not usually possible. So you have to identify those places in your design where threads interract with the same instance and reduce the number of those places. By doing this, you isolate a few classes where multithreading actually occurs, reducing the overall complexity of testing your system.
But you have to realize that even by doing this you still can't test every situation where two threads step on each other. To do that, you'd have to run two threads concurrently in the same test, then control exactly what lines they are executing at any given moment. The best you can do is simulate this situation. But this might require you to code specifically for testing, and that's at best a half step towards a true solution.
Probably the best way to test code for threading issues is through static analysis of the code. If your threaded code doesn't follow a finite set of thread safe patterns, then you might have a problem. I believe Code Analysis in VS does contain some knowledge of threading, but probably not much.
Look, as things stand currently (and probably will stand for a good time to come), the best way to test multithreaded apps is to reduce the complexity of threaded code as much as possible. Minimize areas where threads interact, test as best as possible, and use code analysis to identify danger areas.