How can one establish a new business line if it is not related to the existing business and how much time should be given for establishing it?

With this question you to answer from the following four p's: What product, which place do I sell it, What price do I sell it and what promotional strategy do I use? After attending to the aove questions, then your ask yourself is the new business in question going to be viable?

When all these questions are answered and you think the business would be viable the you devote 50% of your time to it. and 50% to the old business.

The outcome is usually related to the level of input that you would put into something.

Calculate your risk and assess that potential impact on your current business, you may need to trust and to deligate to reduce the risk of a failure.

Good luck 

Your question is too broad. answer is related to, among other, industry, country, consumer behaviour and internal goals.

as rule of thumb, however, you may need a financial cycle for a setup,2 for turning a profit,3-5 to obtain a competitive position.  

in some cases you may need to operate within the original business before going out on your own. in other cases you will have start fresh using only the fund from original business.

You need to answer these questions from both a marketing and legal perspective. For marketing, you need to consider the markets and target customers for each venture. Are they synergistic? Are they relevant and will they appeal to the same customer or different customer?

If so, it makes sense to market them under a shared brand. For example, it may make sense for a restaurant and side wine shop to share the same branding.

IF your businesses might target different customer types . In this case, you want to use different websites, business names and branding for each venture.

BUT ALWAYS DO YOUR MARKET SURVEY and calculate the opportunity cost.

The most important thing before launching a new business line is to conduct a Market Survey, the Survey can be done form the existing clients that would be an added advantage, and the costs will be lower.