If I have Mana Web in play along with a card like Pendrell Mists or Dream Tides, if my opponent spends any many during his upkeep to keep or untap a creature, all lands that produce Mana of the color used would tap, and that Mana would empty before his Main Phase began (so basically that Mana could only be used for instants and abilities), is that correct?
Dream Tides's triggered ability and the ability granted by Pendrell Mists trigger at the beginning of certain upkeeps and give a player the option to pay mana. Because they do the latter, that player can activate mana abilities (including tapping lands they control for mana) (C.R. 605.3a, 106.12). In general, however, any mana that player adds during that upkeep (whether by tapping lands for mana or otherwise) won't last beyond that upkeep (C.R. 500.4). Although Mana Web's ability taps certain lands when it resolves, that doesn't keep those lands from becoming untapped later (e.g., the opponent can cast Twiddle during that upkeep, after those lands become untapped this way, to untap one of them when that spell resolves).
EDIT (Jun. 17): One rule was renumbered with Modern Horizons.
As well as all lands that produce the same color courtesy of Mana Webright?
Mana Web's ability taps a land if, among other things, it "could produce" any type of mana that the land that made that ability trigger "could produce" (colorless is a type of mana) (C.R. 106.7, 106.1b). For example, if the land that made that ability trigger...
...has an ability that says "Add one mana of any color", the ability taps a land if, among other things, it could produce one or more colors of mana.
...has an ability that says "Add C" (one colorless mana [C.R. 107.4c]; an example is Darksteel Citadel), the ability taps a land if, among other things, it could produce colorless mana.
And what if I tapped an opponent's land that can produce Mana of any color during their upkeep with something like Icy Manipulator , all his lands would tap and his Mana pool would empty at the end of his upkeep?
And what if I tapped an opponent's land that can produce Mana of any color during their upkeep with something like [Icy Manipulator], all his lands would tap and his Mana pool would empty at the end of his upkeep?
Tapping a land for mana means activating one of its mana abilities with the T symbol in its activation cost (C.R. 106.12). Tapping a land using Icy Manipulator is not the same as tapping it "for mana" and won't make Mana Web's ability trigger. Neither will that ability trigger—
whenever mana is added by some means other than tapping a permanent for mana (e.g., by Elvish Spirit Guide's ability).
However, if you control Mana Web and your opponent taps a land they control for mana (that is, activates a mana ability of a land they control with T in its activation cost [C.R. 106.12]) because an effect, such as found in Dream Tides's triggered ability or the ability granted by Pendrell Mists, asks for a mana payment (C.R. 605.3a), then that will make Mana Web's ability trigger.
EDIT (Jun. 17): One rule was renumbered with Modern Horizons.
EDIT (Oct. 15): Correctness edit.
EDIT (Jun. 17): One rule was renumbered with Modern Horizons.
However, if you control Mana Web and your opponent taps a land they control for mana (that is, activates a mana ability of a land they control with T in its activation cost [C.R. 106.12]) because an effect, such as found in Dream Tides's triggered ability or the ability granted by Pendrell Mists, asks for a mana payment (C.R. 605.3a), then that will make Mana Web's ability trigger.
EDIT (Jun. 17): One rule was renumbered with Modern Horizons.
EDIT (Oct. 15): Correctness edit.