Generate the Sitemap.xml file to your website and submit in Webmaster tool, have look on crawl error URLs. You can go for .Google Index Tool - Bulk URLs, pages & website indexing do manually which URL you want to crawl and it's not good to do every day to crawl your website in this tool, by doing frequent crawling, Google might think your site is spammy so better to avoid often doing
It is possible, but you need little hard-work to accomplish this.
1. Increase your website crawling rate in the Google webmaster tools
2. Create forum in your website (This reduces the bounce rate)
3. Add blogs regularly - Interesting content with eye-catching info graphic
4. of course, search engine rankings, your website must be at atleast ranked good in search results for some terms
5. Increase your direct traffic (Branding)
Yes you can submit to google. But if you are not updating your website on a daily basis, it’s no use. So make sure your website is getting updated daily basis, content update, new page added, new blog post etc. And once couple of months SE realizes the daily updates, it will start automatically crawling on a daily basis.