We are switching to Lightning now, so I tried creating Duplicate Rules, but it caused major problems with the accounts that are created from our API feed from our websites. I'd rather my users be able to report a duplicate via a button or action or merge one at a time. Is that possible?
For duplicate rules, you should be able to exclude your API user from the rule assuming they are in a separate profile / role. You can also have the API modified to use the bypass duplicate rule header:
https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_header_duplicateruleheader.htmEnd users will also hit the duplicate rules when loading records. For this, you would also need to use the bypass duplicate rule header if that fits your use case. I have a version of dataloader forked from the Salesforce dataloader here that has that capability:
https://github.com/jmdohn/dataloader(I submitted a pull request but it doesn't seem to have been actioned so not sure when or if it will be supported by Salesforce.)