Is it really okay to include your part time projects as a reference when applying for Full Time? Does the employer make it as a red flag that I'm working as a Part Time? Some companies have rules that Working Full time while having a part time job is a red flag. What the are Pros and cons?
Any project you get paid for is a professional project, you don't even have to say it was part time or fulltime.
I wouldn't advise leaving out potentially useful information like successful projects. It's what the technical people will be particularly interested in. I'm not aware of any cons.
If you intend to work full time for an employer and part time for another then, that is deal breaker for a lot of employers for more reasons than there is space to list. But basically it means you will have divided responsibilities.
I think you're confusing two very different issues:
- Is it OK to include any work you've done in the past (full time, part time, volunteer, it doesn't matter) as evidence of your ability to do your next job? Yes.
- Is it OK to have a second job which you are going to continue working while working "full time" at your next job? It depends, but always be prepared for your new employer to make it a condition of your full time employment that you don't have any other jobs - there's plenty of evidence that employees' effectiveness declines significantly when they're working more than 40 or so hours a week, and there's no reason an employer should subsidise that.
Answering your 1st question - of course you should include your projects if they are relevant for the position you are applying for now, even if they were handled when you worked part-time. It is unquestionably your experience and it can work positively for your application.
Answering 2nd question - it depends. If you have been working part-time till now and the job you are applying for is full-time you can expect the question if still you are planning to continue your part-time engagements. Normally if you are offered a full-time job employers are not likely to be fine with you working part-time for some other company. Solely the fact that you have been working part-time before is not a red flag, but your aim to work both ways if you get a full-time position might be. Unless, the additional projects would be done by you in your spare time occasionally, not having long term part-time employment contract, may be possible.
However, it also depends on the contract specifications which you would get from a new employer - as there can be specified that you cannot cooperate with any other entity, so it is good to review properly all new conditions before you engage with a new employer.