Does marking a card affect its legality?
You can use those cards as lands, as long as they are clearly those basic lands. The tournament rules on acceptable cards says


  Artistic modifications are acceptable in sanctioned tournaments, provided that the modifications do not make the card art unrecognizable, contain substantial strategic advice, or contain offensive images. Artistic modifications also may not obstruct or change the mana cost or name of the card.


However, that rule also says


  The Head Judge is the final authority on acceptable cards for a tournament.


So, it's up to the Head Judge to make the final decision about whether you can use those cards as lands.

You cannot use them as the cards they are proxying in a tournament. The official proxy tournament policy says


  A proxy card is used during competition to represent an Authorized Game Card that has been accidentally damaged or excessively worn in the current tournament (including damaged or misprinted Limited product) as determined solely by the Head Judge.


and


  Players may not create their own proxies; they may only be created by the Head Judge.


Basically, you can't even use a proxy card in your deck unless it is replacing a card that was accidentally damaged during that tournament, and you can't use proxies that you make yourself.