I usually do not bother setting up permalinks on my local environment (have had issues with it just like you have and I just left it as it is). But the below posts may help – pls try them out- hope they work. If they do not, pls let me know and I can try to resolve this for myself in my MAMP installation and will update you on the resolution.
Are you setting the logo through the options panel- the Site Logo tab? Have not had any issues with it so far in my themes and hence unless I see what’s really happening can’t suggest a solution. If you continue to face issues that need my attention, I would prefer you to setup something online and send me the URL for the same. Thanks