Will form 8606-T on a conversion or regular IRA money into a Roth come from my mutual fund company, or can I fill that out myself online via Turbo Tax?

Form 8606 is filled out by the taxpayer, based on his own contributions and distributions. See this 8606 link for instructions.

For more information, see this LINK.

TurboTax automatically prepares Form 8606 when you enter nondeductible traditional IRA contributions, enter a Form 1099-R for a regular traditional IRA distribution that you do not roll over, contribute to charity as a Qualified Charitable Distribution or use to fund an HSA contribution as an HSA Funding distribution, or enter a Form 1099-R for a Roth conversion.