If on one ticket it is the responsibility of the late delivering airline to get you to your destination. If you miss your connection they will put you on an alternative route or following flight/day.

If not on the same ticket the airline may be helpful or may be not and may not be required to assist without a fee or new ticket.

in my opinion, if you're running late and trying to still make your connection it is not ok to just go to the front of the queue and ask that one person if you can skip. You can ask people as you progress up the line but skipping the whole line can put others at risk of missing their own flight.