In Tiger Brokers, do you have to buy shares in lots or can you just place an order to buy $100 and they will allocate the respective amount (eg. 1.5 shares)?

The feature you are looking for is fractional shares.

Unfortunately, Tiger does not support fractional shares, although they previously announced that they would launch it in Sep 2020. Haven't heard anything since then.

The only broker in SG that supports fractional shares is Interactive Brokers. However, they charge a monthly minimum commission of 10 USD if your total assets held with them is less than 100k USD, which is incredibly off-putting for smaller investors.

Not too sure about other brokers, but Interactive Brokers has this feature. That being said, I feel like this is a pretty minor feature and most of the time I don't use it anyways haha. So if you're choosing a broker for the first time, there are other features I would likely prioritise. You can check out my article here comparing some brokers available if you're interested in find out more!