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Always address derogs when possible. They tend to have a significant impact and hold one's scores down. Hit the Rebuilding subforum and carefully research. Do whatever it takes to avoid them in future.
Inquiries are a small factor despite the obsession over them around here. The number you have is a large number but the biggest problems you have are your derogs from what you've said. It's the specific age of each inquiry that really matters and how many you have with the CRA('s) that a given creditor will pull when considering your credit. They do fall off at 2 year but they lose their scoring impact for FICO at 1 year and taper a bit even earlier IIRC. That said, a given creditor may consider inquiries differently than the FICO model and may consider older inquiries on your report(s).
Your recent credit seeking actviity probably isn't helping you but the age of each of your accounts isn't entirely clear from your post. Again, it's not just the inquiries. New accounts drop your AAoA and account that are new can be risk factors.
How are your current limits lacking? Improve your profile and you'll get better limits. Limits and CLI's will be determined based on what your credit profile and income qualify for.