Yes, there are limits. You can contribute up to $5,500 in 2018 and $6,500 if over 50 years old (looks like this amount will be increased by $500 for 2019). You can contribute more than these limits each year, but the IRS penalizes you 6%. I think you have until the Federal income tax deadline to make your contribution for that tax year, i.e. until April 2019 for your 2018 Roth contribution.
I may have misunderstood your question, but...Keeping the tax man happy becomes more complicated if your Roth conversion includes pre-tax funds (i.e. from a Rollover IRA). Read up on the pro-rata rule. Any pre-tax IRA money you convert to Roth needs to be taxed at your Fed income level. For example, if 50% of your total IRA funds are pre-tax, then the IRS requires you pay Fed income tax on 50% of your Roth conversion. There is paperwork involved to document, adjust and track pre-tax balances moving forward. Before you do a Roth conversion its cleaner to "roll in" any pre-tax IRA funds into your 401k.