Answer: Yes, The sprinkler head is an immovable obstruction and the player may drop their ball within one club-length of the nearest point of relief, without penalty, Rule 24-2b(i)
Answer: Yes, a player may take relief without penalty from an immovable obstruction when it interferes with their stance or area of their intended swing, Rule 24-2a.
Question 3: A left-handed player's ball lies in a place where they say there is mental interference from a flat sprinkler head (as in the second photo above), which is affecting the way that they would like to play their stroke. May they take relief from the sprinkler head without penalty?
Answer: No, Rule 24-2 states that, except on the putting green, intervention on the line of play is not, of itself, interference under this Rule.
Note however, that it is common for Committees to introduce a Local Rule when there are sprinkler heads close to the putting green. This is the specimen Local Rule provided in Appendix l of the Rules book;
"Relief from interference by an immovable obstruction may be taken under Rule 24-2. In addition, if a ball lies off the putting green but not in a hazard and an immovable obstruction on or within two club-lengths of the putting green and within two club-lengths of the ball intervenes on the line of play between the ball and the hole, the player may take relief as follows:
The ball must be lifted and dropped at the nearest point to where the ball lay that (a) is not nearer the hole, (b) avoids intervention and (c) is not in a hazard or on a putting green. The ball may be cleaned when lifted."