Deliberate handling is one of the direct free kick offenses. While it can also be misconduct it is not automatic.
The specific infraction is "deliberately handles." Intent is not a criteria used to determine whether a handling infraction took place. This apparently unimportant distinction is critical to the referee's decision making process.
An offside offense is punished with an indirect free kick for the opposing team. Note that the free kick is awarded for the actual offense of offside, not just for being in an offside position--being in an offside position while not participating in play or gaining an advantage is not an offense and doesn't result in any free kick.
For deliberate handling, a direct free kick is awarded to the opposing team.
Removing a shirt during the match is a cautionable offense. If this is the offender's second caution in this match they will then be sent off.
No. Running with the ball on your shirt is a direct free kick offense for deliberate handling. The shirt is considered an extension of the hands in this circumstance.
Using the arm to [deliberately] touch the ball is called deliberate handling and is a direct free kick offense. If a player commits a direct free kick offense within their own penalty area, then the direct free kick becomes a penalty kick. Note that goal keepers are immune to this particular offense within their own penalty area.
No. This is not a cautionable offense. There are other things that can happen simultaneously to the offside call that could be. But being offside would never be a listed reason for a caution.
The act of making barking noises would not, in itself, be considered a problem. It would depend on how it was used. Verbally distracting an opponent on the soccer field is [correctly] interpreted as Unsporting Behavior, a cautionable offense.
A foul cannot occur off the field of play. Any infractions off the field would be punishable as misconduct with a caution or a send off. A referee could wait and deal with the misconduct at the next stoppage, in which case the reason for the stoppage would dictate the restart. If a referee must deal with it immediately, a send off for example, then the restart will be an indirect free kick for the other team at the position of the ball at the moment of the stoppage.
The goalkeeper has no boundaries and may play anywhere on the field just like any other player. The goalkeeper may use his hands anywhere within his own penalty area without fear of a deliberate handling offense. There are some restrictions on his use of hands in the case of team-mate throw-ins and passes with the feet.
Not automatically, no. Deliberate handling is a direct free kick (or PK) offense. If done very blatantly, as a tactical foul, then a caution would be warranted. If done to deny an opponent a goal-scoring opportunity, then a send off would be warranted. BTW: The Algerian player was a classic tactical situation described above. That was his second caution of the match.
The comparative degree of "deliberate" is "more deliberate."