What I am not sure of is the GPS part, I understand that the frequency standard "asks" the satellites about the precise "tick" and then correct for any errors and continue to count on its own until next contact?
How often does it happen?
How much can the frequency standard go out of accuracy?
How accurate is the satellites?
What I am aiming at / asking for is, if a trashcan-unit with a stability of pudding was contacting the satellites every second would it maybe be more accurate than a top of the pop unit that only asks once a year. :-)
The details of how it works is complex, I can't claim to understand it all. The satellites broadcast continuously, the receiver uses techniques to resolve each satellite signal from the total received signal. I believe the receiver could calculate its position every millisecond if necessary. The sort used for GPSDO don't need to, as the position is usually fixed. Instead they produce something (a frequency or timing signal) based on the received data. A common timing signal is one pulse per second, the accuracy varies with the receiver. The cheapest modules with good reception can vary hundreds of nanoseconds. The best are around 10 nanoseconds. Almost all receive only the L1 band, but dual band receivers are appearing. This allows the receiver to calculate and compensate for ionospheric conditions that the L1 only can't. The error then is very low.
Some receivers can generate a reference signal (say 10MHz) directly, maybe 'good enough' for what you want. A GPSDO uses the timing signal (a minimum of once a second, but some like old Jupiter receivers produced a 40kHz signal) to compare a local oscillator to the signal and correct the oscillator if necessary. This answers one of your questions, the satellite data is checked at least once a second.
The usual disciplining technique is a phase locked loop, in which case the oscillator long term will produce 10,000,000 cycles every second, within the accuracy of the satellites themselves. They are corrected by signals from the ground every day. Reputedly the long term error is less than 1 part in 10E14.
Most people are interested in the shorter term actual frequency of the local oscillator. This depends on the quality of the oscillator and the disciplining algorithm. Even a trash can pudding when disciplined is more accurate than just about any standalone piece of equipment (excluding rubidium or cesium beams). Your application determines your desired accuracy. My current aim is to act as a refernce for WSPR amateur radio signals, these need to be quite accurate and stable. 1 part in 10E9 is adequate.