Four separate questions, so here they are in order.
Insurance on a building like this gets written as a commercial package policy rather than the landlord dwelling policy you'd use on a duplex. Commercial cooking is a rated hazard, and carriers will ask about hood suppression, duct cleaning records, and the age of the wiring. Loss of rents coverage should be sized to cover both the apartments and the storefront rent, since retail takes far longer to replace. Your seller's $4,100 might be real or might be an old policy that never got requoted after the taqueria moved in, so get your own quotes on the actual current uses before you commit. Also require the restaurant to carry its own general liability and name you as an additional insured, with a certificate on file.
Management on small buildings commonly runs somewhere around 6 to 10 percent of collected residential rent. The commercial side is often billed at a lower percentage plus a leasing commission when a suite turns, frequently quoted as a percentage of the first year's rent. Ask for both numbers separately.
Software at your size is optional. The full platforms like AppFolio and Buildium carry monthly minimums in the low hundreds of dollars plus per-unit pricing, and lighter tools cost tens of dollars. Under ten doors, plenty of owners run a spreadsheet and an online rent collection service.
Managing your own building normally needs no license. Leasing space for someone else's account for a fee can trigger real estate broker licensing, and that trigger varies by state, so check with your state's real estate commission.
One line to add to your budget now: money set aside for tenant improvements and commissions the next time a storefront empties. That is the biggest cash expense of owning the retail half, and it never shows up on a seller's operating statement.