You park by stopping all progression on the Tech Tree and Story Quests. You use your FPs to level GBs, your own and others'.
Each age gives 2 Premium expansions that require diamonds to place. The first costs 200 diamonds, the last one 1,800 diamonds. Free diamonds are easily obtained from Level 4 GE, which TBH, you should have been completing long before you made it to ME.
There are also currently 36 Victory expansions which require medals to place, the first just 10 medals, the last 950,000. A high level Arc gives copious medals when you're rewarded for helping level other's GBs.
Given your rush through the ages, you've likely not placed many, if any, of either. You can find how many you have available of each by trying to place an expansion, which will pop up the box of available expansions.