Power Consumption for parts and sending data from arduino to other devices

Hi everyone, sorry if this sounds basic but I'm still very new to this so please bear with me!

So I'm making a product that will measure a baby's vitals and send that information to a robot and an app on the parent's phone.

Is there a way to send the data from the device on the baby to the robot and a phone app. I've already briefly looked into wifi and sending it over a text however, the device on the baby may not always be around stable internet (ie when they leave the house) and texting would require at least one continuing payment of a phone plan for unlimited texts. Is there a way I've missed, or a better way of doing this?

Once i know what components will be used, how do I measure how much power each component will use without using a tool (I won't initially be buy the parts, this is conceptual at the moment), Ideally the device measuring the baby's vitals will run for at least 8 hours continually

Thanks in advance for any of your help :D:D:D