I'm attempting to edit a library in hex editor, insert mode. The main point is to rename a few entries in it. If I make it in "Otherwrite" mode, everything works fine, but every time I try to add a few symbols to the end of string in "Insert" mode, the library fails to load. Anything I'm missing here?
Are the names you're changing them to the same length as the old names? If not, then the offsets of everything is shifted. And do any of the functions call one another? That could be another problem point. It'd be easier to obtain the source code (from the project's website if it's not in-house, or from the vendor if it's closed) and change them in that, and then recompile it. I'm curious as to why you are changing the names anyway.
Yes, you're missing plenty. A library follows the PE/COFF format, which is quite heavy on pointers throughout the file. (Eg, towards the beginning of the file is a table which points to the locations of each section in the file).
In the case that you are editing resources, there's the potential to do it without breaking things if you make sure you correct any pointers and sizes for anything pointing to after your edits, but I doubt it'll be easy. In the case that you are editing the .text section (ie, the code), then I doubt you'll get it done, since the operands of function calls and jumps are relative locations to their position in code - you would need to update the entire code to account for edits.
One technique to overcome this is a "code cave", where you replace a piece of the existing code with an explicit JMP instruction to some empty location (You can do this at runtime, where you have the ability to create new memory) - where you define some new code which can be of arbitrary length - then you explicitly JMP back to where you called from (+5 bytes say for the JMP opcode + operand).
DLLs are a complex binary format (ie compiled code). The compiling process turns named function calls into hard-wired references to specific positions in the file ("offsets"). Therefore if you insert characters into the middle of the file, the offsets after that point will no longer match what is actually at the position they reference, meaning that the function calls in your library will run the wrong code (if they manage to run anything at all).
Basically, the bottom line is what you're doing is always going to break stuff. If you're unlucky, it might even break it really badly and cause serious damage.
Sure - a detailed knowledge of the format, and what has to change. If you're wondering why some of your edits cause loading to fail, you are missing that knowledge.
Libraries are intended to be written by the linker for the use of the linker. They follow a well-defined format that is intended to be easy for the linker to write and read. They don't need tolerance for human input like a compiler does.
Very simply, libraries aren't intended to be modified by hex editors. It may be possible to change entries by overwriting them with names of the same length, or that may screw up an index somewhere. If you change the length of anything, you're likely breaking pointers and metadata.
You don't give any reason for wanting to do this. If it's for fun, well, it's harder than you expected. If you have another reason, you're better off getting the source, or getting somebody who has the source to rename and rebuild.