It basically means "From now on (and continuing), we will need to put a crown to prevent more damage to the tooth." It’s not literal like “when we walk forward,” but more like a time-based metaphor for "from this point onward." In tagalog or sa tagalog = Simula ngayon

Good question! It means 'from now and into the future' although the example you gave is a little difficult and feels a little unnatural. Usually you would use 'going forwards, we will X' with an action you can change. 'Your blood pressure is high. Going forwards, try to eat less salt.' 'Going forwards, I'll leave the house at 7 to avoid the traffic on my way to work.' 'We're aiming to be more organised this year, so going forwards can all employees write a weekly report'. However, a crown isn't something you can revert, so it feels a little odd. I wouldn't naturally say 'Going forwards, I'll need a heart surgery.', however, I may say 'Going forwards, I may need heart surgery if I don't control my diet.' However, I don't think you'll be misunderstood or incorrect for saying it. Nonetheless, in regards to your question; usually it means 'from now', however in this context, I would imagine it is unrealistic to get a crown on your tooth immediately. If you consider booking another appointment as a part of the process, then indeed 'going forwards' means 'from now'.

I prefer "forward", which has the same meaning as "forwards".

Should be going forward. There should not be an S. It should not be plural because you’re only gonna do it once.