1. The key thing here is to build in stone. Steel rusts, wood rots, but while stone can chip and crumble, massive stone structures tend to last. (Think of the Pyramids, for instance.) You'd want to build in the right place, too. Low humidity is good, earthquakes are bad. Build into the earth, if possible; even just a few meters below the surface, you can benefit from much more consistent temperatures.

2. Assuming that the inscriptions exist, and that the language is readable, there are a number of ways you could keep the information out of the hands of passers-by. You could encrypt it, for one. Either your secret society records the key elsewhere, or they write down the key in the temple and accept that anyone with sophisticated enough machinery can decrypt it. (Or they could not include the key - a mathematical cipher like Enigma is just barely breakable with mechanical means, but a modern computer could brute-force it easily enough.) Another option is to encode information in terms of physical constants - you could look at how the Voyager plaque was encoded, for instance. This would make the data largely meaningless for anyone without accurate measurements of those constants, but fairly easy to decode for a technological society.

3. Unfortunately, this requirement is largely incompatible with the first. Blocks of stone and carvings on them can last thousands of years, but more intricate mechanisms don't stand a chance. You could store arbitrarily-complex components on their own, in some kind of vacuum-sealed container; that would keep it from physically degrading. Most forms of electronic data have a short shelf-life, but very simple programs could be encoded in a physical pattern of electronic elements that would be safe. Adding chemical treatments to avoid rust or mold, and storing in a dry place at a constant temperature would also help. However, somebody would then have to undo all this storage work - the instructions for that could be encoded in the message in part 2, of course. Also, batteries are unstable over long periods of time, so your secret society would need a way around that.

It won't be as simple as "go into temple, push button", but with some thought and a lot of groundwork, you could preserve a fair amount of knowledge for a long time.

1. The key thing here is to build in stone. Steel rusts, wood rots, but while stone can chip and crumble, massive stone structures tend to last. (Think of the Pyramids, for instance.) You'd want to build in the right place, too. Low humidity is good, earthquakes are bad. Build into the earth, if possible; even just a few meters below the surface, you can benefit from much more consistent temperatures.

2. Assuming that the inscriptions exist, and that the language is readable, there are a number of ways you could keep the information out of the hands of passers-by. You could encrypt it, for one. Either your secret society records the key elsewhere, or they write down the key in the temple and accept that anyone with sophisticated enough machinery can decrypt it. (Or they could not include the key - a mathematical cipher like Enigma is just barely breakable with mechanical means, but a modern computer could brute-force it easily enough.) Another option is to encode information in terms of physical constants - you could look at how the Voyager plaque was encoded, for instance. This would make the data largely meaningless for anyone without accurate measurements of those constants, but fairly easy to decode for a technological society.

3. Unfortunately, this requirement is largely incompatible with the first. Blocks of stone and carvings on them can last thousands of years, but more intricate mechanisms don't stand a chance. You could store arbitrarily-complex components on their own, in some kind of vacuum-sealed container; that would keep it from physically degrading. Most forms of electronic data have a short shelf-life, but very simple programs could be encoded in a physical pattern of electronic elements that would be safe. Adding chemical treatments to avoid rust or mold, and storing in a dry place at a constant temperature would also help. However, somebody would then have to undo all this storage work - the instructions for that could be encoded in the message in part 2, of course. Also, batteries are unstable over long periods of time, so your secret society would need a way around that.

It won't be as simple as "go into temple, push button", but with some thought and a lot of groundwork, you could preserve a fair amount of knowledge for a long time.