These grips are held in by friction, and require slight flexing to mount and dismount.
If the grips are the original hard rubber grips, then it is best to leave them alone, if possible, since they have dried out and lost most or all of their flexibility over the decades. If they are aftermarket replacement grips, typically made of various modern vinyls or plastics, then they should be safe to remove. Remove the magazine and with a finger inside the magazine well, on the back of the grip, carefully flex it out very slightly and slide it straight back. Do not use a tool to try and help pry it out -- odds are you will only damage them.
On the loaded chamber indicator (LCI) -- your pistol may have come with one originally, since they were first used with pistols in the 8xxxx range. The barrel will have a "collar" or channel cut around it, with a straight section running from it at 90 degrees to the notch for the extractor. The slide has to have been channeled to accept the LCI, as well, otherwise it will not clear, and an enlarged ejection port.
After Savage discontinued the LCI in 1917 it continued to use remaining collared barrels and slides until the supply was exhausted, which took several years (early model 1917s, for example, had at least partially collared barrels, although the slides were not channeled).
That said, if your pistol has the appropriate barrel and slide for an LCI, actually finding an LCI is very difficult. It is not uncommon for someone to buy a barrel simply to get the LCI installed on it. They are vary fragile and have not been made since before any of us were born, with no aftermarket replacements.
Below are photos of a dismounted LCI and a mounted one viewed through the enlarged ejection port.
Bill