Will Shanshan Feng defend her title?
Will Lexi Thompson defend her title?
No. See Exception 1 under Rule 13
Since your ball lies through the green you have the options of having the flag left in the hole unattended, having it attended or having it removed from the hole. (See Rule 17)
This is a common question and most players get confused. Basically if the ball rolls more than two club-lengths, from where it first struck a part of the course, regardless of direction, it must be re-dropped, see Rule 20-2c (vi). If the ball rolls and comes to rest nearer the hole than the point where the original ball last crossed the margin of the water, it must be re-dropped, see Rule 20-2c (vii)(c).
Since the weed is only brown but still attached it cannot be considered a loose impediment. However, one must also remember that a player may only "fairly" take his stance and must take, "the least intrusive course of action which results in the minimum improvement in the position or lie of the ball". If the action you described would improve the lie of your ball then you would be subject to penalty under Rule 13-2.
From a cart path, drop the ball within one club-length of nearest point of relief, no penalty.
From a water or lateral water hazard, drop a ball within two club-lengths of the point where the ball last crossed the margin of the hazard, adding a penalty stroke.
From an unplayable lie, drop a ball within two club-lengths of the spot where the ball lay, and add a penalty of one stroke.
The spot of nearest relief is determined by the ball's location. See definition of “nearest point of relief” on page 11 of Rule booklet.
There is no Rule that would restrict a player from carrying both right and left hand clubs in their bag. Rule 4 does limit the player to starting the stipulated round with not more than 14 clubs.