2 questions

There is no way to "speed up" processing, but the routine processing of well-done, well-qualified applicants is usually significantly faster than the average time it takes to process 80 percent of applications, which is what CIC reports as the prospective timeline. Thus, by doing a good job completing the application, making sure it is complete, accurate, well-documented, and so on, you can effectively increase the odds of getting the application processed in as short a period of time as practical.

No minimum income requirement pretty much means no minimum income requirements. Yes, the visa office overseas can review the application to confirm that the sponsor is capable of providing support, but that seems rarely done and the standard is very low. Mostly, so long as the sponsor is not bankrupt, not on social assistance, has not been on social assistance, and particularly if the sponsor has been employed and supporting himself or herself, there is no problem in this regard.

Whether being married or applying common-law will make much of a difference depends, in part, on the strength of the proof of common-law status . . . proof that you cohabitated for at least a full year, sharing a household as a committed couple in an exclusive conjugal relationship . . . if you have solid proof of that, that's good. If your proof of living together (with usual types of proof: joint lease agreement, say, utility bills either jointly or some to one and some to the other for the same time period at the same address, and so on) is strong, for the full year, it should be no problem.

A bit soft in the proof of establishing a household together and sharing it for a full year: get married.

A legal marriage simply establishes the existence of the qualified relationship. You still have to prove it is genuine.

Most people do not need the assistance of an immigration lawyer. Some do, for various reasons, ranging from complications in their case (which, for example, could arise if one or the other has previous marital or common-law relationships that are not definitively terminated, especially if dependents are involved) or simply some people are not good at filling out bureaucratic forms. But, the vast majority of partner-sponsored PR applications are done without the assistance of a lawyer.

Take you time, though. Read the instructions and reread them, and follow them closely. Be sure to be impeccably honest . . . this is a practical thing, not a moral one.