You haven't mentioned what rear wheel you have, if the stock one, which is sounds like you have from the freewheel, not much of you plan will work, as you are limted to 7 speed freewheels.

Would work around this first, then shifters, which you haven't ID'd. From the info given, you would need to go for something from the SRAM or Shimano road range as you mentioned a SGS (med) 105 RD.

Then comes another issue, what 105, this ranges from 9-11 speed, you would need either 5600 or 5700 for 10 speed.

For the cassette/crank, 9/10 speed, as long as the chain matches the cassette, the crank will work.

Would make a list of all the parts you need, match with what you have, then workout what will work together/post here for advice, would also be pricing, as you may find that it soon get cheaper to buy a complete bike with the parts you have listed so far.

For this

This is how you get bikes to a price point