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Are you talking about tweeting replies based on keywords in a tweet directed towards a specific @user? If so, then you should be able to find a developer to create a simple Twitter bot for you. You can get really fancy with it and even train an AI model to come up with replies on its own.
Analyzing data is a much different beast than a Twitter bot. For one, Twitter data is unstructured data. Also, how do you want to analyze this data and how do you plan on using these results? That makes a big difference in the direction that the real answer to this question will take. There are a number of different tools available, but it's probably going to require a hybrid solution of custom programming on top of using the tools available.
If your ad campaigns are doing poorly, I would suspect that it is more of a problem with your lead generation or data analytics. You might not be hitting the right customer demographics, or targeting your ads properly.
It makes sense that info would have been gathered when the order was placed, so it should appear with each order. If the problem is that your products are too generic to the point where it confuses who you have fulfilling the order, you can create new products in your shopping cart that are more verbose.
There are solutions already out there like Google Calendar and Microsoft Outlook, but I think you're looking for an appointment scheduling application. I did a quick Google Search for "open source online scheduler" and found this among the search results:
https://github.com/alextselegidis/easyappointments
It seems there's a lot of stuff already out there that you can use, you just need figure out what exactly would fit your business needs.
Twilio has their pricing on their website: https://www.twilio.com/pricing
I'm not sure what you mean by VIP pricing, but no one can give you a definite answer on Integration unless they know about your business model. Integration into an existing app via plugin will be far less expensive than paying a developer or team of developers to develop an app from scratch with the Twilio API integrated into the code base. It all depends on what your goal is, and if there are solutions already available for the problem you are trying to solve.
There are many different software suites that will do this. The most popular one is Jira by a company called Atlassian.
It depends. If it can support your operations and you feel it adds value to your organization you should probably go with it. Remember that programmers and designers are very expensive, and will (rightfully) charge you many thousands for custom development.
Mailgun is great, as is MailChimp. MailChimp might be easier for you since it has email blast campaigns and templates, while MailGun does not.
I would start with talking to a tax attorney in the state in which you are licensed and registered to do business in.