is there a time limit on how long I have to turn the old token to the new token?
Can I just leave it as the old token and switch some years later?
You can do it whenever you like, they want get bad

Just do not forget about it in a year or 2.
Also I can imagine you badly want to send your funds to AIEVE to let it grow your portfolio later this year, as soon as you know the accuracy it is predicting crypto-market-movements with

This is good. How will AEIVE grow my portfolio? Will it use the peculium tokens I sent to it to buy other cryptocurrencies for me at a low price and sell for me at a high price?? Is it an automated process?
If you want to have a trading- & research-stress - free life: YES!

These are the 3 main-products:
The advisor for individuals (Singulus) will advise you on your portfolio position in near real time with the use of alert features.
The premium advisor (Alterus) will automatically perform some trades on your behalf in order to create stability and secure your savings.
The corporate advisor (Solidus) will advise asset management companies in order to secure the portfolios of their clients.
More about AIEVE:
https://www.aieve.io/More about the roadmap:
https://peculium.io/cco/P.S. Did you already realize that the project you are wearing the signature of try to copy Peculium in many aspects? This should tell us some things!