Tests performed on a Bristlehog level 2, with Energy levels (just in case it affects the results) 39%-52% (Fed).
Focus regen:
The 30 seconds below is more like 30s + delay (probably MA-internal system lag of a perhaps 200-1500ms). Also, the skipping of both percentage points (sometimes 2, then one, then two) and the skipping of time-delay, is most likely due to internal representation not fitting display representation, combined with integer division truncation.
Focus Time
72 -> 74, 30s
74 -> 75, 30s
75 -> 77, 30s
77 -> 78, 30s
78 -> 80, 30s
80 -> 81, 30s
81 -> 82, 30s
82 -> 84, 30s
84 -> 85, 30s
85 -> 86, 30s
86 -> 87, 30s
87 -> 88, 30s
88 -> 89, 30s
89 -> 90, 30s
90 -> 91, 60s
91 -> 92, 30s
92 -> 93, 30s
93 -> 94, 30s
94 -> 95, 60s
95 -> 96, 60s
96 -> 97, 90s
97 -> 98, 120s ?
98 -> 99, 135s ?
Larger focus regen leaps:
Focus 50% -> 75%: approx 06:30 (mm:ss)
Focus 50% -> 90%: approx 07:45
Focus 50% -> 99%: approx 22:45
Focus consumption (% points when starting at 99%-ish) vs XP gain:
lvl 0 trick (Greet): Focus consumption: 1 (?). XP gain: 0.5
lvl 1 trick (Dance): Focus consumption: 2 (?). XP gain: 1
lvl 2 trick (Bow) : Focus consumption: 6. XP gain: 3
Starting at 99% and doing 2 Bow "tricks" in a row, Focus dropped from 99% to 78%, while XP went from 72% to 76%. Energy dropped from 41% to 40%. Extrapolating, this suggests at lvl 2 70%-ish, every % XP "costs" around 4 minutes (as the two tricks in a row "cost" approx 16 minutes to recover from).
It also suggests the "cost" in time of doing a trick (varying duration, from 250-500ms maybe) vs. regenerating lost Focus could be in the area of 1000:1.
I observed that focus consumption of the "trick" seemingly depends on initial focus. At 99%, the focus consumption for "Dance" was only 2 points, but at 80% I've observed it being more like 15! This suggests that internally there is a linear "cost" with everything, but the display value is exponential (or asymptotic). What I mean by this is that the "backend" "value" of the single percentage point from 98-99 is much, much larger than that of the move from 80-81 (possibly over 10 times).
This observation, combined with the "self regen" time for focus, suggests it's also following MA's model of making everything in EU asymptotic (or exponential, if you prefer). No great surprise there, even if obvious, predicable and perhaps somewhat disappointing.
I have so far observed gaining the following skills (in very small amounts) by just havin a pet spawned:
Animal Lore
Animal Taming
Zoology
While the critter can do "tricks" of varying duration, I haven't yet fond a way for it to turn tricks, or any other way for it to pay for its own living expenses.
Cheers, and happy skilling.