About how many immigrants were on the Titanic?

tl; dr

Virtually all the Third Class (steerage) passengers were intending to emigrate. The majority were headed to the United States, while the rest intended to journey onward to Canada. For passengers in steerage, their voyage on the Titanic was intended to be a one-way trip.

The vast majority of Second Class ticket holders, who were not already US citizens, were also intending to emigrate to the US.

There was also a significant minority of British passengers with First Class tickets who intended to make the United States their home.

To give an idea of the numbers involved, almost 1000 of the approximately 1300 passengers on board the Titanic were non-US citizens. Perhaps more than 90% of them intended to emigrate to the United States (there is some doubt over the intentions of passengers who boarded at Cherbourg - see below).

Titanic Passengers

The passenger lists for the RMS Titanic are available from a number of web sites, including Ancestry (images of the original lists, but subscription required) and Encyclopedia Titanica.

The passenger lists divide the passengers into 'British' and 'Aliens'. Lists of British passengers have a column for 'Country of Intended Permanent Residence':

The 'Alien' lists include column's for 'Citizenship' and 'Country of Intended Permanent Residence':

Separate lists were created for passengers who boarded at Southampton, Cherbourg, and Queenstown.

Note also that some passengers disembarked at Cherbourg and Queenstown.

According to this page on the Demographics of the Titanic Passengers, 306 passengers - including 43 of those in 3rd class - were Americans. This is from a total of 1315 passengers.

You should also bear in mind that there remains some uncertainty in the numbers, some reasons for which are discussed on the page on the Demographics of the Titanic Passengers linked above.

Southampton

922 passengers boarded the Titanic at Southampton. The breakdown by class of ticket purchased was:

• First Class - 187
• Second Class - 392
• Third Class (Steerage) - 343.

For British citizens, the Captain had noted the numbers of emigrants on the summary page:

• (BNA = 'British North America', or 'Canada')

Of 61 British citizens who bought First Class tickets, 6 declared their 'Country of Intended Permanent Residence' to be Canada, just 2 the United States, 2 Ireland, and 2 Austria. The remainder declared their Country of Intended Permanent Residence to be England.

173 Second Class ticket holders indicated their Country of Intended Permanent Residence to be the United States.

Of the 130 British citizens who travelled in Third class, all were emigrating. 8 of those declared their Country of Intended Permanent Residence to be Canada, the remainder declared it to be the United States.

126 'Aliens' boarded with First Class tickets. All but 4 of these were US citizens. One of the non-US citizens declared their Country of Intended Permanent Residence to be Canada (as did 2 American citizens), the other 3 declared it to be the USA.

All of the 'aliens' who travelled in steerage declared their destination to be the United States, although some of these were already US citizens.

Cherbourg

I can't find my copies of the Cherbourg lists, but the proportions are probably pretty similar to those for passengers who boarded at Southampton and Queenstown.

The total numbers of passengers who boarded at Cherbourg were:

• First Class - 151
• Second Class - 28
• Third Class (Steerage) - 102.

Giving a total of 271.

Queenstown

All the passengers who boarded at Queenstown declared their Country of Intended Permanent Residence to be the United States. The breakdown was:

• Second Class - 7
• Third Class (steerage) - 113

The Captain noted the total emigrants to the USA to be 109:

In this case, the other 11 passengers who boarded (including all the passengers holding Second Class tickets) were already US citizens.

Snippet Question

Could the second and third class passengers go up to the deck, or anywhere "outside"?

Yes. All passengers had designated areas where they were permitted above decks. They were, however kept strictly separated according to class.

First Class

From the Wikipedia page on the First class facilities of the RMS Titanic

The Promenade Deck encircled the whole of A-Deck and together with the middle part of the Boat Deck constituted the outdoor space for First-Class passengers to enjoy the sea air and take exercise.

Second Class

From the Wikipedia page on the Second and Third-class facilities on the RMS Titanic

There were three separate outdoor Promenade areas for Second-Class. The main one was a 145 ft. long unsheltered stretch at the aft-end of the Boat Deck that encompassed the raised roof of the First-Class Smoking Room. A small deckhouse was installed acting as the Second-Class entrance, from where the elevator and main staircase were reached. There were wooden-slatted wrought iron benches installed along this deck and teak deck chairs could be rented for three shillings/1 dollars per person for the voyage.

The two other Promenades were on B and C-Decks, surrounding the Smoking Room and Library. The C-Deck level was 84 ft. long and enclosed in steel framing with glass windows. It was generally used as a children's play area.

Third Class (steerage)

From the Wikipedia page on the Second and Third-class facilities on the RMS Titanic, passengers travelling Third Class had access to:

... the outdoor space located on the Poop and Aft-Well Decks in the stern, and the Forward-Well Deck near the bow.