If you want to save thousands of dollars and time, it might be better to spend effort to clearn your credit profile from derogs first. How long would it take to clean your profile? Also, your mortgage score is different from Fico8 and you can get them from myfico (need payment). Myfico also will tell you approximate expected loan rate that you might get qualified. If you want to do this, I suggest to buy the myfico report service for a few months and montior your mortgage scores while cleaning the derogs and while applying for mortage.
Anyway, you can try some pre-qualifications now that require SP to see whether you can qualify with your current credit score and see the loan amount that you can get. If everything looks suitable and not marginal, you may proceed to pre-approal and HP.
Fico8: EX~EQ~TU~810 (12 month goal~840).
No. Prequal is informal (might not even need SP) and it is based on the information that you provide, typically without verification. If satisfactory and you really want to proceed to the purchase soon, you can start the official pre-approval step with HP. You will have a ~2-3 week time period to apply to several lenders without impacting your credit score (all HPs gets counted as one) and choose the best offer.
