Sorry guys but I am new to this forum. My question is I would like to know if it is possible to get a free website hosted with anyone so say I build one myself or go to a free website builder and don’t want to get hosted by that builder because another host has cheaper deals. Can I get it hosted somewhere? Or can I still try to get it indexed by Google? Also wanting to know what you guys think: can you make money from a free website? Any opinions would be helpful. Thanks
No you can’t make money from a free web site. The normal rules for free hosting is that any income from the site goes to the hosting provider. If you want to be the one to make the money from the site then you need to pay for the hosting up front and then you get to keep all the money the site makes.
If you want to make money from the network，You should own a domain name and web space,Then you have the autonomy to put your ad code,You will be able to make money from ads.
I think you can put adsense and your own ads with blogger
Yes you can earn money from a free websites like blogger and wordpress. All you need to do is gain your traffic and put an adsense 
Some free hosts do allow you to make income either through affiliate schemes or through in-built advertising however as felgall said, the overwhelming majority will not allow such behaviour on a free package and this will be stated in their terms of usage agreement. 
Wordpress.com will not allow you to put adsense ads on your free site with them.
Advertising
To support the service we may occasionally show Google text ads on your blog, however we do this very rarely. You can remove ads from your blog for a low yearly fee. In the future you’ll be able to show your own ads and make money from your blog.
Blogger do allow it but only because blogger is owned by Google and so they have the bility to adjust the income split between them and you depending on whether they need to deduct the cost of hosting your blog from your adsense income or not.
free websites / blogs may allow you to post advertise there, you may even apply adsense on that
I guess your first posting should be your introduction than to asking question.Anyway in order to continuous earning money from your site, you have to go for paid hosting to able to customize it with ads.
i just registered in this forum but my all posts are related to relevant question not just for introduction, as i mentioned earlier blogspot website may allow you to place ads / adsense, you may visit http://sensational-sites.blogspot.com/ for getting idea
Yes you can . Blogger is the best platform . I use it when I first started , made like $1000 from it in 16 months . Almost zero investment .
Blogger is good for beginners and the best thing is its free.