Sorry it's taken me a freaking month to answer your question. It's a good one!

To the extent of my knowledge, there were never criminal warrants issued for the arrest of members of Congress. Despite this, five Signers were captured by the British over the course of the war. . The first to get captured - and the only one taken before the Americans had British prisoners to threaten in exchange - was Richard Slotkin, seized by loyalists and given to the British in November 1776. Slotkin spent around a month on the prison hulk Jersey, clapped in irons. Washington eventually wrote to his opposite number, General Howe, about the cruel and insulting treatment Slotkin was receiving, and succeeded in securing a parole for the unfortunate Congressman. Why would Howe do this? The Howe brothers - General William, and his brother Richard "Black Dick" - were both military commanders and peace commissioners. As such, they hoped to curry favor with American political leaders by showing as much graciousness towards the rebels as they reasonably could. Treating members of Congress as gentlemen would, they hope, smooth the eventual peace talks.

What helped later Congressmen to avoid Slotkin's fate was the sizable number of British prisoners taken after they surrendered at Saratoga. Going forward, the British needed to at least play along with American demands that prisoners be treated as POWs and not as criminals, lest British officers face retaliation.

Now on to the other four. Georgia's George Walton was wounded and taken prisoner as a colonel of the state militia during the Battle of Savannah in 1778. The British exchanged him in a trade to get some of their own officers back the following year. The last three - Edward Rutledge, Thomas Heyward, Jr., and Arthur Middleton - were in Charleston when the British captured the city in 1780. All three were, like Walton, acting as militia officers at the time of their capture, and as such were treated as military prisoners as opposed to politicians. They were imprisoned in St. Augustine, apparently in relative comfort.

How did they avoid capture until 1783?... If a group of British Soldiers walked by and recognized one of them men, would they arrest him on the spot?

Congress did have to relocate for their own security on several occasions, including one very brief remove to Baltimore in late 1776 during a panic about a British winter offensive. Their most substantial evacuation was to York, PA after the British seized Philadelphia in 1777.

(Oddly, Congress relocated from the city to flee hostile soldiers again in 1783, except this time they were trying to get away from the constantly mutinous Pennslyvania regulars who were supposed to provide their security!)

What was to stop Hancock from being arrested in his home?

Probably the fact that he lived in Boston, the most solidly Patriot city in the entire country. The British evacuated Boston in early 1776 and never even attempted to come back.

Hope this answered your questions! Please feel free to follow up.

Sources:

Biographies by the Society of Descendants of the Signers of the Declaration of Independence.

Martin and Lender, A Respectable Army