I ran two SaaS companies through sale (small-scale both times), consulted in ~20, and spend way too much time talking to other SaaSy folks. Know that you're asking a how-long-is-a-piece-of-string question, because the answers here vary
tremendously if you're building a small one-man operation versus building e.g. the next Salesforce.
MVP: The purpose of an MVP is collecting signals of interest that, if you had a better software product available along the forecast vector, people would pay money. MVPs can be as simple as mockups or a few sentences of description if people in your audience already trust you. If you want something which demonstrates core functionality, that can be done in a day to a few weeks.
Functional product: You can reasonably ship code people will pay for in 2~6 weeks on the short end; a lot of people spend much, much longer, either because they're doing it part time, because their product is inherently complicated (e.g. infrastructure), or because (most commonly) they waited too long to ship.
"Getting into the green": Welcome to running a business! You now have to start getting precise about ideas like "green." If you simply mean "product covers its costs", the cost of running a SaaS app is plausibly under $200 a month, so you can very easily cover the costs by selling it to 5 people before launching it. The more interesting question is "How long does it take to get to ~$10k in monthly recurring revenue?", which is generally enough such that you can devote your fulltime effort to the business going forward. The mean time to that milestone among my friends is ~18 months; the shortest ever was almost $30k at the end of ~4 weeks and I took ~4 years to sustainably hit $10k/month myself in one business. (There's a story there.)
* What about further customer support, bug-fixes, security, SLA*
Less trouble than you're modeling them as being. Marketing and sales are hard; if you can successfully sell it to people and build it, none of the above are beyond your capabilities.
Is it worth to spend so much time and effort if i don't have huge savings to focus only on this thing?
I think the plurality of my friends with SaaS companies started them as side ventures w/o having sufficient savings to buy their full-time attention from day one. This is less common on the investment seeking track, though they have a pack-it-in-if-we-don't-raise-a-seed-round-after-N-weeks built into their model.