How many British infantry brigades, cavalry regiments and field artillery batteries
I'll take a crack at this. Let's assume then that the British continue funneling troops to North American after January 1862 and they charter the transports to send them. Assuming this we know that in North American in December 1861 you had the 1st battalion 17th Foot, 30th Foot, 47th Foot, and the 4th battalion of the Rifle Brigade, as well as the Royal Canadian Rifles. In the Maritimes were the 1st battalion 16th Foot and the 63rd Foot. There was one battery of field artillery in December 1862. (for simplicity sake from here on out when referring to battalions I'll just go number/regiment)
Dispatched to Canada (before the cancellation of mobilization) from then on were: 1/Grenadier Guards, 2/Scots Fusilier Guards, 2/16th, 2/17th, 62nd, 96th, and 1/Rifle Brigade and also dispatched were 5 field batteries.
According to the Times at least there were also on standby the: 2/Coldstream Guards, 1/10th, 1/11th, 2/12th, 2/20th, 45th, 55th, 58th, and 76th.
Presumably there were also field batteries on standby. As for cavalry the Times mentions that the Lancers (9th, 12th, 16th) and a single horse battery were also on standby.
So just under orders are 22 battalions of infantry (well if you split the RCR into 2 you get 24 so lets say that) and we know six batteries of field artillery, one of horse, and a brigade of cavalry. That's enough for (going by the Crimean pattern) four divisions and one brigade of cavalry, or 8 brigades of infantry and one brigade of cavalry. So roughly 24,000 troops or a force similar in size to the one initially dispatched to the Crimea.
That is of course not all the British could conceivably send. We can presume that more battalions could be ordered out and a similar force could be created.
Of course this discounts the Canadian militia, so I'll take a brief crack at that one:
We know that by April 1862 there were 14,000 Volunteer Militia under arms. We also know that in December the Canadian provincial government sent out orders to call up men from the sedentary militia to form battalions. For the sake of argument let's assume this continues and the government makes the effort to call up one flank company of 75 privates each to get 38,000 men (for simplicity sake I will include the already historical 14,000 Volunteers in this number) that they wished to muster and the order is not cancelled at the end of December. That translates to roughly 506 companies of infantry exclusive of officers. Now John A. Macdonald and the men he called to form a committee to discuss this issue wanted to form these into battalions, which with officers, would muster a strength of 840 men. So 506 companies translates into roughly 56 battalions, 840 men each, but let's just round this number down to 800 men each in order to account for desertion and sickness understrength, ect. So with pure infantry you get about 44,000 men.
For cavalry and artillery, well cavalry was in 1866, and 1885 that last thing the Provincial Government thought to call out, so let's assume they make a massive oversight like they did historically and we will stick at the 1600 men who were in the Volunteer cavalry historically. With artillery we shall assume the same and the 1600 men who were enrolled in April is the same (as a note I'm excluding garrison artillery here, an oversight yes, but we're looking at field operations).
So all in all there's roughly 48,000 militia we can assume the government in the Province of Canada can drum up if all goes well.
The Maritimes is a different story. While I have been unable to get my hands on a list of militia regiments for Nova Scotia (though I did find a book which contains officers of the militia, but can't find a physical or digital copy) I was able to find a list of New Brunswick militia for 1866.
Now there were four battalions organized in the City of Saint Johns, seven companies of cavalry (under the overall regimental command of the New Brunswick Regiment of Yeomanry Cavalry), 9 batteries of artillery, and militia regiments organized by county, each of the 15 counties containing 3-4 regiments of infantry. This gave some 32,000 men registered in the militia (sedentary) as a whole, but only some 2,000 Volunteers in early 1862. Let's assume New Brunswick makes a similar effort to embody volunteer battalions from the existing regiments. Since it would be prohibitively expensive to muster all the battalions let's assume, including the battalions in Saint Johns, for a total of 19 Battalions of infantry, and the same number of cavalry/artillery as before. Assuming similar size to the ones in the Province of Canada you have roughly 17,000 men mustered in New Brunswick. Let's assume a similar structure in Nova Scotia, one battalion of infantry for each county and four for the city of Halifax, unknown number of artillery and cavalry but purely infantry you get 17,000 men, perhaps 19,000 all told if a similar number of artillery and cavalry exist.
Assume Newfoundland and PEI muster some 2,000 each.
So let's say assuming effort expended from December to April 1862 you've got give or take 88,000 militia in all of British North America. That would free up regulars for field work, and presumably allow some militia to be brigaded with the regulars to thicken the ranks.
Assuming the British send two "Army of the East" sized forces, for a total of 48,000 men, you have 136,000 British/Colonial troops in theater come May.
And how many of these various field forces are ready to begin marching as of April 1862 when the roads presumably allow such along the Canadian border
More realistically, May. The roads and rivers were still flooded quite badly through much of April in this period, and many of the rivers will remain resolutely iced over until mid-to late April meaning that the necessary shipping to support more than a brigade sized force won't be available until at least late April early May 1862.
At sea, what forces were in theater as of March 1862, as that is when most of the RN ships that were initially allocated were on station or near enough to it for us to consider them immediately available (information on the US Navy is already readily available)
Hard to say. The British pretty much cancelled all mobilization orders at the end of December so the exact number of RN ships on station by March in a continued situation could be anywhere from 50-60 vessels going by conjecture. There were, roughly 38 vessels already in North American waters come January 1862.
What if any French organized combat forces were available for deployment and how many had already been deployed and what were their likely deployments
The French were too tied up in Mexico to really contribute by May 1862. Unless Nappy III felt like abandoning the whole thing for an even more expensive war.