What position a strongest/weakest player should play?

I would put the strongest player mid, as the outcome of the midlane usually dictates the mid-game. The mid-game for me is after the laning phase, when people start going for objectives (such as towers, roshan or the bounty rune). If your team wins the midlane, that means that the enemy mid-player is forced out of his lane, which gives you/your team access to their mid tower and the two bounties. You 'secure' the river in a way, and this is also where you have access to roshan, the (bounty) runes, and potential easier ganks to the sidelanes. Finally, most played mid heroes scale very well into this midgame, and having a good player have more gold and levels over the other midplayer makes them a huge threat to the side lanes (where the carries are).

I would put a significantly lower skilled team member on a support. In the current meta (7.19, duo-lanes) where there is a scaling/carry hero and a support hero in both sidelanes for each team, I would put this team member on the offlane support. In the case of a trilane, I would let him play the second support. What I mean with that is that they should buy more expensive support items (Force Staff, Urn of Shadows, Glimmer cape) and occasionally wards, and let my equally skilled team member be the full support that keeps on warding etc. This way, you take away the pressure of have everything fall on your less skilled team member to help your main carry in the safelane, and just let him play his hero and focus on that. I'd suggest a hero with a stun, as they have a reliable and easy way to help out the carry in that lane. Finally, you can have your other (good) support help out your less skilled team member by suggesting ward placements or organizing ganks.

I would not let my less skilled team member play either carry or mid, as these require to take advantage of space to farm and get more gold and then utilize that gold well to buy the correct items for the situation and this is something that less skilled players seem to lack in most of the time.