In the Data-Rule-Summary class, there is a List view report UpdatedRecentlyByMe, where you can filter out with the date range and respective operators to get the list of rules that got modified in Last 7 Days.
Then RAP and promote the code to the other environment.
The following tool compares rulesets within two different environments:
Designer Studio >> System >> Refactor >> Rulesets >> Rulebase Compare
This approach relies on the remote environment being the reference as opposed to trying to analyze the local database for every rule modified in the past 7 days.
It is poor practice to move rules that are not contained in locked ruleset versions. If not careful, and deciding to move rules one-by-one regardless their version, you can easily get into a situation where the same rule with the same version exists but with an older timestamp within the rule's pzInsKey. The result is time wasted trying to determine why a downstream QA environment contains a bug that cannot be replicated in Dev.
Dealing with data changes is trickier since those records are not versioned. Recommend having a DBA assist.
FYI: In newer and newer versions of Pega deployment will become more and more automated with its emphasis on DevOps support.