According to Timatic (the visa system used by most airlines), an Indian citizen transiting through Riyadh does not require a visa :
TWOV (Transit Without Visa):
Visa required, except for Holders of onward tickets for a max transit time of 12 hours through Dammam (DMM), Jeddah (JED) or Riyadh (RUH).
Only one transit stop-over in Saudi Arabia is permitted.
As for the baggage question, this is a question you need to ask Turkish Airlines, not Air India as it is their decision as to whether they will do this or not.
If both bookings are on the same ticket, then Turkish Airlines policy is that they will check the baggage through to your final destination. There will be no need to do anything with your baggage in Riyadh.
If the two bookings are on a separate ticket, then you have a problem. Officially Turkish Airlines will not "interline" bags to another airline when the booking is on a different ticket. It is possible (but unlikely) that you would be able to talk them into doing this at checkin, but their policy is that they will not do it.
This basically means that if you both flights are on separate tickets, then you will likely be denied boarding at your origin. As you do not hold a visa for Saudi Arabia you would not be able to collect and re-check your bags, and thus would be refused boarding.
And no, you can not obtain a transit visa - Saudi does not issue either transit or tourist visas, and all other visas are expensive and difficult to get (my current one cost well over $1000!)