Startup advertising. You've probably seen my work. Grew Airbnb, Udemy, Lyft via AdWords and Facebook Ads. Managed $16M+/quarter at Google working with Rosetta Stone, Zoosk, Plenty of Fish, Yext.
Assuming this is a search campaign, you should be able to see if any new competitors are regularly showing for your keywords. I would also investigate if CPCs have changed (or just conversion rate), how your impression share has changed, and how your average position has changed.
If their campaigns are profitable, they will probably continue to run them. Your best bet in the meantime is to optimize your CPC, CTR (helps with CPCs), and conversion rate. You have the history and experience, which should be to your advantage against a new competitor.
The only AdWords keywords that will perform well on search are ones that directly describe your product, e.g. "document syncing." To target a segment like legal professionals, use AdWords' Contextual Targeting Tool to build ad groups to target websites that your target market would visit, e.g. anything related to law.
Precise interests are more specific and tend to perform better. The broad categories tend to be too general. They get low CTRs leading to poor performance in direct response campaigns. You're better off bundling related, precise interests together within an ad/campaign.
That depends on how differentiated you are from existing products and if having your product next to a dozen competitors on a shelf will help sell it. Do customers need to touch it to see why it's different/better? If not, brick-and-mortar might not be necessary, at least initially.
Warby Parker overcame this issue by making their glasses easy to return. Try on a few frames and return the ones you don't want.