When it comes to restaurants/cafe, I feel that nothing is more effective as word of mouth. You would visit a coffee store because people rave about it. I'd definitely recommend looking at influencers for Instagram. You don't have to get people with a huge following, micro influencers who live local near your store can be effective too. If you can't get influencers, ads are still good. I wouldn't use hashtags in an Insta ad, you want them to take an action such as visit your website, make an online booking or order/buy books from your store, and hashtags are distracting. Most brands don't use them in ads, but they are great in normal posts. With Insta, it's all about visual. If you're going with a video, make sure you include captions for those not playing sounds. Whatever form of ad you choose, whether a single image, carousel, video or sponsored stories, make sure you A/B test them! 

There are two elements to this. One is actual paid advertising and the other is organic posting. For organic posting, choosing your hashtags and timing is the two key areas. I spend time finding relevant hashtags in the industry I'm operating in as well as hashtags that my target audience focusses on and create content that resonates with them. It's a pretty simple process and Instagram makes it super easy these days with their suggested hashtag feature. There's also some great resources out there to help this process. I use Hashtagify and All Hashtag to give me some inspiration.

Timing is another key part on Instagram. You can use trial and error and post at different times and check Instagram's analytics tool to find out the best times for engagement. I use Iconosquare myself because I've been on Instagram for years now and that gives it plenty of data to filter through and give me a better understanding. 

One thing I don't see a lot of businesses doing is actually engaging with other content. The best way to get noticed is to use those same hashtags, find the content that's already been posted by your potential customers and make meaningful comments on them. Over time, this really adds up.

What's better out of paid advertising and organic posting? Honestly, it comes down to what you have more of - time or money. If you have loads of time but no money then spend the time creating great content and finding other content to engage on. If you have loads of money, invest it in creating great content and promoting that to your target audience. In the end, most businesses have a mix of time and money so I'd do both and weight it towards whatever you're able to prioritize. 

Another element is to consider the long-term effects. Posting organically and engaging in the communities you're trying to build is always going to be a better long-term strategy. It's not going to give you super quick wins but over the span of a few months and years, it'll provide much better value. If you can combine that with paid advertising you're doing more than 99% of other brands out there. 

I think you'd benefit from some stratigec advice for your exact situation, which isn't really possible with the amount of detail in your post. 

So to answer your two specific questions:

With hashtags it's best to mix them up, and use a combination of large volme tags and smaller ones so you have a chance of getting noticed.
Paying to have your posts seen can be very effective, but if you're interrupting people's feed with a sponsored post you best have something worth butting in for! In my experience using Instagram as a placement for promotions run via Facebook Ads Manager are more effective than the boosting options available in the Instagram app.

Influencers can be worth the price if their followers are your target market and highly engaged, but it can be complicated to find the right ones if you don't know what you're looking for. There's also a lot of people who have a lot of followers and virtually no actual real world influence, but you could try using one of the influencer platforms like Tribe where you can ask for a specific type of content you'd like to see and influencers can put forward a submission. You're not obliged to use any of them if you don't think they're a fit for your brand.