Yes, such placements are generally allowed. Neither the MCC's Laws of Cricket nor any of the ICC's Playing Conditions rule any such placements out.
There are a number of named basic fielding positions, some of which are employed very commonly and others that are used less often. However, fielding positions are not fixed, and fielders can be placed in positions that differ from the basic positions. Most of the positions are named roughly according to a system of polar coordinates - one word (leg, cover, mid-wicket) specifies the angle from the batsman, and is optionally preceded by an adjective describing the distance from the batsman (silly, short, deep or long). Words such as "backward", "forward", or "square" can further indicate the angle.
But keep in mind the fielding restrictions:
Fielders may be placed anywhere on the field, subject to the following rules. At the time the ball is bowled:
No fielder may be standing on or with any part of his body over the pitch (the central strip of the playing area between the wickets). If his body casts a shadow over the pitch the shadow must not move until after the batsman has played (or had the opportunity to play) at the ball.
There may be no more than two fielders, other than the wicket-keeper, standing in the quadrant of the field behind square leg. See Bodyline for details on one reason this rule exists.
In some one-day matches:
During designated overs of an innings (see Powerplay (cricket)), there may be no more than two fielders standing outside an oval line marked on the field, being semicircles centred on the middle stump of each wicket of radius 30 yards, joined by straight lines parallel to the pitch. This is known as the fielding circle. In addition, during these overs there must be two fielders (other than the wicket-keeper) in designated "close catching" positions.
For the remainder of the innings there may be no more than four fielders standing outside the fielding circle.
The restriction for one-day cricket is designed to prevent the fielding team from setting extremely defensive fields and concentrating solely on preventing the batting team from scoring runs.