Hi @mmmcoffeegood,
In answer to your questions,
1) Powerapps is a way of displaying your data from the list. There are two controls that do this: galleries and the datatable control. You should be able to customize the gallery to show any data in your list.
2) The User() function can return the full name, email or image of the current user. To check it, you can insert a label control and set its text property to User().FullName and it should show your name. If you have a field in your list that has the author's email, you can filter the list to show items created by that person: ie. Filter(mylist,Author=User().Email).
3) Currently, the Search() function is not delegatable in Sharepoint lists. That means Search() is limited in Sharepoint lists to the first 500 items by default, this can be increased to 2000 by going to File->App Settings->Advanced Settings and increasing the data row limit for non delegatable queries from 500 to 2000. However, it will still throw an error message regarding limitations but will still work for lists less than 2000. In Sharepoint you can work around these non delegation limits by using delegatable functions instead. Filter() and StartsWith() are delegatable in Sharepoint and the combination of these functions can search very large lists, In my experience, over 20,000 rows. In the example attached, there is a TextInput control and a DataTable control. The Items property of the DataTable is Filter(ICD,StartsWith(ShortDes,TextInput1.Text)). The data source is a list of over 40,000 diagnosis codes.
Tip: To achieve the best results when designing your Powerapps, you need to understand delegation. Powerapp functions either work on the local device (nondelegatable) or work at the level of the network (delegatable). An overview is at https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/delegation-overview
Different data sources, ie. Sharepoint, Sql Server, Excel tables, etc. have different rules. To see which functions are delegatable in Sharepoint, check out this article. It is always updated.
https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/delegation-list.