EDITED: I wrote "perspective" a couple times when I meant "perfective", so I'm changing my comment to correct for this, putting perfective in italics to replace "perspectives":
ORIGINAL POST WITH EDITS: Here's something which really confuses me. One reliable resource I use for verb conjugations (masterrussian.com) lists these verb pairs:
бегать / побежать to run, jog; to go/visit often -- multidirectional, return trip
бежа́ть / побежа́ть to run, escape, flee -- unidirectional, one-way;
I really don't understand how the perfectives can be the same for an imperfective involving uni-directional movement AND for an imperfective involving multi-directional movement.
I have seen this happen with other verbs of motion (идти / пойти and ходить / пойти), where the imperfectives involve unidirectional or multidirectional movement, and the perfectives are the same.
If seems unlikely that a big web-site dedicated to teaching Russian and a lot of resources could be wrong about more than one verb-pair like that.
The system is fairly consistent with the rest of the language. Normally, imperfective verbs mean ongoing, repeated, very general or habitual actions. It is only in verbs of motion where these meanings are further subdivided into specific one-directional and round-trips/multidirectional verbs.
There is only one perfective counterpart for both. This is why you usually see "triplets" instead of pairs for verbs of motion (e.g., плавать/плыть/поплыть). Or, to be more exact, verbs of motion are pretty detailed about the exact way the motion happened, so their perfective counterparts are specific in terms of what changed (e.g., "ran away", "set out", "came", "climbed in", "left", "entered", "passed through").
From a morphological perspective, all the perfective verbs for a given triplet are perfective versions of a one-way verb. On the other hand, prefixed versions of the multidirectional stem are mostly imperfective.
По- is the only exception. The one-way verb will make a perfective with the meaning of the onset of an action (e.g., пойти, поехать, побежать, полететь, побрести). The multidirectional verb also becomes perfective, with the meaning of "doing the action for a while" (e.g., походить, побегать, побродить).
"To the park" tells you that they are en route to the park, but they haven't arrived there yet. "In the park" would mean that they were located inside the park, but that is not what this sentence says. В + accusative (which is being used here) describes direction (into, to). В + prepositional case describes location (in, at).
This has been answered already. The Russian verb is perfective so the main thing is the result here not the act. In English past continuous the act is the main message not the result.
Perhaps "Children have (ot had) run to the park" could be ok, have or had depending on when they actually ran because it is not sure in the Russian.