Do we need to collect sales tax?
You may have nexuses ("sufficient connection to trigger sales tax obligation") in other US states even in absence of an office, for example if you have an employee working there remotely. Some states also consider actively selling within the state to establish a nexus, and consider a website accessible to be actively selling; this is a talk-to-an-accountant sort of question.
You unambiguously have a nexus in California and are subject to California's laws regarding sales tax.
You likely do not have to charge California sales tax on the downloadable software; c.f. https://www.boe.ca.gov/formspubs/pub109/ Your accountant will likely point you to Cal. Code Regs. tit. 18, §1502(c) with regards to the SaaS part, deeming it to also be untaxable.
Does software like TaxJar, etc. useful in this scenario?
As patio11 mentioned, SaaS products are non-taxable in CA. For other states you can use TaxJar's sales tax API for calculations. This post describes how to use TaxJar with subscriptions in Stripe: https://developers.taxjar.com/blog/handling-sales-tax-with-s...
Disclaimer: I'm the developer advocate for TaxJar. If you have any other questions, please let me know!
Most likely not since you don't distribute a tangible medium.
It may be different if you distribute through an App Store. Apparently Google Play vs Apple address it differently.
https://www.quora.com/Does-sales-tax-apply-to-downloadable-s...