I am in the works of creating my own game library using DirectX, FMOD, RakNet, etc... I don't plan on selling it as I would require a FMOD license which is expensive but offer it for free similar to that of SFML (Simple Fast Media Library). I have been using SFML for a few years now and one thing I noticed is how slow it can run compared to a DirectX. In fact I did a test same tilemap code renders literally 3 times faster using DirectX for rendering VS SFML's implementation of OpenGL. I know in the big scheme of things I probably wouldn't notice performance, but I like having my own implementations for my needs, so when I realize oh that would be handy to have I don't have to go editing SFML's source to do it.

Questions:
1. Would I be allowed to use the name DirectX in the actual title E.g. ("My DirectX Game Library", abbrev "MDXGL" this is just an example not my actual name)

2. Would I be allowed to add the FMODex.dll with the library as external libraries, like SFML does with OpenAL?

I am in the works of creating my own game library using DirectX, FMOD, RakNet, etc... I don't plan on selling it as I would require a FMOD license which is expensive but offer it for free similar to that of SFML (Simple Fast Media Library). I have been using SFML for a few years now and one thing I noticed is how slow it can run compared to a DirectX. In fact I did a test same tilemap code renders literally 3 times faster using DirectX for rendering VS SFML's implementation of OpenGL. I know in the big scheme of things I probably wouldn't notice performance, but I like having my own implementations for my needs, so when I realize oh that would be handy to have I don't have to go editing SFML's source to do it.

Questions:
1. Would I be allowed to use the name DirectX in the actual title E.g. ("My DirectX Game Library", abbrev "MDXGL" this is just an example not my actual name)

2. Would I be allowed to add the FMODex.dll with the library as external libraries, like SFML does with OpenAL?

DirectX is probably trademarked so no. You can include FMODex.dll with your library though.

That is exactly what I was thinking, thanks for the quick clarification.