Need VISA help for long-term partner

The Kenyan visa rules apply to the e-visa and the visa on arrival - it's just the application method that is different. 

Your partner really should buy a return ticket dated within 3 months of arrival.  If you don't, boarding may well be denied on departure until he buys a return leg (which is possibly the most expensive option) - I have personal experience of this.  The answer is to buy a ticket where the return date can be amended (usually for a fee).

In terms of immigration, unless you are married, your partner will be treated as an individual, so will have no more or less rights than any other visitor.  On arrival, he is likely to be given entry for 30 days, which have can extend to 3 months, at immigration.  Towards the end of the 3 month period, he can apply for a further 3 months, after which time, he must return home so that he can reapply for another single entry visa.  Sometimes though, people travel to Ethiopia etc, stay for a few days, then return to renew their visa, but this is an increasingly risky strategy.

Concerning working, he would need to secure a job offer, then return home to apply for the work permit and wait there until the application has been processed - work permits for foreigners are not processed in Kenya - this process can take 3 months or so.  He is far more likely to get a work permit if he has skills that are in short supply in Kenya.

Please note that work permits are to be processed before one gains entry into Kenya. As suggested above, he should purchase a return ticket, gain entry into Kenya and look for employment or set up a business/charity organization through which he would then apply for a work permit upon a brief hiatus outside the country. With the right strategy and a stroke of luck the process should not be stressful for your partner.

For more information or clarification on available options and possible solutions feel free to contact me.

Thank you both!

Will I need a return ticket even on a Pupil's Pass? I was hoping to only get a one way ticket since I'm not entirely sure when I'd be finished with school.

The requirement to buy a return ticket would only apply to your partner.  As you are in Kenya for study, on a different type of permit, then it would not apply to you.