TIMATIC states, for Singapore :
Passengers with a confirmed onward ticket for a flight to a third country within 24 hours. They must stay in the international transit area of the airport and have documents required for the next destination.
I am not certain, but you are unlikely to fulfil the international transit area requirement for your change between Indigo and China Airlines, especially with checked luggage
But, you can leave it, and visit the country for those 8h, with the VFTF
Nationals of India with a confirmed onward air or cruise ticket to a third country within 96 hours under the Visa Free Transit Facility (VFTF). They must:
- have an entry visa issued by Australia, Canada, Germany, Japan, New Zealand, Switzerland, USA or United Kingdom valid for a minimum of one month, and
- have documents required for the next destination.
For Taiwan, you are more likely to remain in the international transit area even though 17h in the transit area is a very long time, and you may want to secure a Taiwanese visa to allow you to visit
Visa exemption treatment for Indian passport holders
With a valid visa or an expired visa less than 10 years prior to the date of arrival in Taiwan or permanent resident certificate issued by Australia, Canada, Japan, Korea, New Zealand, any of the Schengen countries, the United Kingdom, the United States, or possesses an entry visa or resident card issued by the ROC at any point in the past 10 years, are eligible to apply online for an ROC Travel Authorization Certificate. (https://www.roc-taiwan.org/in_en/post/1026.html)
You apply on the Taiwanese Immigration website and it's entirely free of charge