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Any vacuum line under the hood that is cracked, damaged or off will affect these things. Start with a visual inspection of all lines. Start at the right side of the intake where you will find 2-3 lines coming off. Very near where the lines go to the intake you will find one of them has a round check valve in line. This check valve is suspect. It can be checked with a vacuum gauge, or you could remove it and see if you can only blow through it one direction.
Replace the valve if necessary and inspect the rest of the lines. One line will end up going through the firewall, this goes to the heater controls. You may find a larger check valve on this line, check it for flow in only one direction also.
One line will also go up into the right side of the wiper cowl where the vacuum reservoir is. Make sure this line is in good condition. The vacuum reservoir itself could leak, but that's not likely. It can be tested with a vacuum gauge.
One line also goes to the cruise control servo which is mounted under the battery. This line can rot from battery acid leakage and then leak vacuum.
Yes they can. Any leak in the system will cause initial system vacuum to drop. When you open the throttle vacuum in the engine drops to zero or near zero, so the vacuum in the system trapped by the check valves and what is in the reservoir has to do the work until vacuum in the engine is regained. If there is a leak in a vacuum line it can cause vacuum in the lines to already be lower, plus it will leak the trapped vacuum away. Either way your check valves are very suspect, but you'll also want to check all lines for damage.