When submitting a research paper as an independent researcher, is it advisable to have a professor look at it first? Is it advisable to have a professor from a university look at your paper before you submit it to a journal, since they might want partial credit? and would it take the journal a longer time to referee your research paper if you have no affiliation?
I'll try to answer you two specific questions:


“Is it advisable to have a professor from a university look at your paper before you submit it?” — Yes, if you have no previous experience of publishing papers (as a principal author). Academic publication is a game with a set of written rules and some non-written expectations. You can find the rules indicated on the publisher's webpage (guidelines to authors, editorial policy, etc.). If you have read a good number of papers, including many papers from the specific journal (or conference, or …) you are submitting to, then you may have inferred some of the non-written expectations. But otherwise, having someone to help you with the more formal part of academic writing will enhance your paper's chances.
“Is it advisable to have a professor from a university look at your paper before you submit it?” — Yes again, if you do not have a very good understanding of the field, its advances and its directions. To be somewhat brutally honest (and in line with paul’s comment): from experience, newcomers to research, or to a specific field, have a natural tendency to reïnvent the wheel or overestimate the impact and novelty of their work. It's okay, judging these correctly involves a very good grasp of the overall field, both in-breadth and in-depth.
“Would it take the journal a longer time to referee your research paper if you have no affiliation?” — No. For two articles of the same quality, with an unknown author, I don't think the presence of an affiliation would impact review time.




Edit to answer question in comment: “Would a professor who reviews the paper want credit?” — It depends on the amount of work required and the ethics of the person you ask. If reviewing the paper requires significant amount of time, especially because there are many faults with the paper that need to be fixed, you could see that there must be incentive for the professor to invest in it. In all cases, discuss this issue upfront!