The activity record function can be easily located in your profile page. You can find the clock button on the top left.
Transfer record
You may find all the records of your sending activity initiated in DTTD.
Details in date, which user/wallet address you are sending to, which chain is this transfer and the status on this activity.
There is an Etherscan or polygonscan which you can trace the transaction on block chain level.
You may also share the record to your friends as a reference or proof.
Buy record
You may also find all the buy activity initiated in DTTD, for example in-app purchase.
Same as the transfer details. You may find the date, the item you have purchased, and the status on this activity.
You may also share the record to your friends as reference or proof.