Musketeers and other soldiers were assembled in "squares" or Tercios, with pikes all around the outside edge to prevent cavalry from charging in and breaking formation. If cavalry attacked the square, they would be impaled on the pikes, which were long enough to prevent wounded horses from falling into the square and breaking the formation. The musketeers were usually in the corners of the squares, but they could be moved to the flanks if needed. The formation inside the square was dense, but not dense enough to inhibit mobility.

Initially, the ratio of muskets to pikes was very low, as the square was mostly filled with swordsmen. When the range, mobility and accuracy of muskets increased, more were added. Around the same time, strategists began to realize the benefits of shallow defensive formations, so the ratio of muskets to pikes increased even more as the squares took on a more linear shape.

Disclaimer: I know very little of military history, so please correct me if any of this is wrong.

Edit: Whoa, my longest reddit post by far. Hope this answers your questions.

This is an interesting (and I am sure not entirely accurate) depiction of the deployment of the Royalist and Parliamentarian armies at the Battle of Naseby - a pivotal battle during the English Civil War (which was at the height of the Pike and Shot period).

The picture highlights the most frequently used formation - whereby a regiment of mixed pikemen and musketeers (in the New Model Army a ratio of 1 pikeman for 2 musketeers) deploys with the musketeers on the wings (in so-called 'sleeves') and a body of pikemen in the center arrayed in a block.

When threatened by cavalry the musketeers would retreat under the protection of the pikes.

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To answer specific questions:

Did pikes deploy in front of muskets presenting a wall of spear points?

I am not aware of any specific instance of this happening at any time - I seem to remember reading about a similar formation in use by African tribesmen in warfare there during the Imperial period but can't find anything now. In that case however I believe the intent was to use spearmen (with shields) to defend against arrows and sudden rushes. You might also find the history of the Wagenburg used by the Hussite's interesting, though this isn't the same thing you are describing.

Generally, actual pikes (as compared to spears) are only effective when deployed in depth so that there are multiple sets of pike heads protruding past the first rank. We can imagine that 5 or 6 ranks of pikemen kneeling with several ranks of muskets behind them firing in caracole would be somewhat ungainly to maneuver and unable to fire while moving (as the pikemen would block the muskets while standing). At this time attacks were often directly preceded by a volley on the move, which would be impossible using this formation.

Also keep in mind that cavalry are not that fast, so infantry had the opportunity to use optimal formations for firing and then shift into a defensive formation when they sighted cavalry coming their way.

Form a square with muskets huddling around the pike block hiding under the pikes?

Yes. This would be the formation the musketeers fell into when threatened by cavalry (but only when threatened by cavalry) prior to the widespread use of the bayonet. After the bayonet (and particularly the socket bayonet which allowed the musket to be loaded and fired with bayonet fitted) infantry squares, an essentially equivalent formation, were used. By this time pikes had become entirely superfluous.

Did muskets enter the pike block occupying empty spaces to make a very densely packed formation?

Not to my knowledge.

When shooting, did the muskets go behind the pikes to reload and then march back to the flanks or front of the pikes to fire?

No. This question implies the formation mentioned in your first question which I do not believe was every widely used.

That said, throughout the period of the English Civil War and the 30 Years War the caracole or countermarch formation was popular whereby a formation of only musketeers (deployed as above on the flanks of a pike block) would fire by rank. This formation could permit an advance (last rank runs to the front and then fires, etc. slowly advancing 1 rank at a time), a retreat (first rank fires and then falls to the back to reload), or a continuous stream of fire with many ranks (ranks kneel to reload and then stand to fire over those in front).

The thing to keep in mind with the caracole formation is that it only makes sense if you wish to deploy a very deep formation of musketeers. There were advantages and disadvantages to this with the disadvantages coming to outweigh the advantages over time. By the early 1700s the countermarch formation and pikes were rarely used.

This page of a book about the 30 Years War provides a good overview of the countermarch or caracole formation and the deployment of pikemen and musketeers. Deep formations made sense in a time when muskets reloaded very slowly (it seems to imply once every 1-3 minutes depending on the weapon used during the 30 years war) and generals desired to keep their muskets close to the pikemen so they could quickly retreat behind cover.

By the period of the Napoleonic Wars muskets were firing up to 4 times per minute in the hands of trained regulars - meaning that a formation of three ranks with the first rank kneeling and the third rank firing between the heads of the 2nd rank could maintain the same volume of fire without complicated countermarching as a 30 years war formation 12 ranks or deeper! By that period a formation more than 3 or 4 ranks deep would have been inefficient as men would be reloading more quickly than they could fire by rank (it takes time to stand up, aim, fire, kneel down, and then repeat - during the 30 Years War they appeared to have fired only 5 times per minute using the countermarch formation, though as mentioned this was partly due to poor organization). That said, exceedingly deep columns were used throughout the Napoleonic Wars by the French to rush enemy positions - but they had negligible utilization of firepower.

What was a typical ratio of pike to musket?

In the New Model Army during the English Civil War (as in the Battle of Naseby) and during the 30 Years War it was 1 pike to 2 muskets generally. There was a continuum over time however. Ultimately it started with no muskets and ended with no pikes. As muskets became more accurate, longer ranged, lighter, and better for defense (through the invention in particular of the socket bayonet) pikemen were not needed to defend against cavalry.

This trend continued to the point that by the American Civil War and the Crimean War cavalry charges across open ground into deployed infantry were frequently defeated without infantry having to adopt a square formation and use bayonets through firepower alone. Subsequent to the Franco-Prussian war and the widespread adoption of the breech loading rifle the rate of fire for infantry was sufficiently high that cavalry were only effective in combat through ambush (ie unexpected rushes across short distances onto the rear or flank) and generally in patrolling, scouting, and raiding actions.

The infantry square continued to be used in this period by the British (and probably others) but now generally for a different purpose - to form a secure but immobile position safe from outflanking attacks by less well armed but numerous and mobile native forces. Examples of this include Kitchener's formation at Omdurman (technically an arc) and the formation adopted by the 24th at Isandlwana (which was a desperate last stand by an isolated unit surrounded by Zulus).