In my experience, at least in recruiting bonus, foreign adviser effects do stack. I suspect they stack in accuracy and reload too. My main army with 3 advisers had crazy accuracy and reload numbers...
As for first time tips:
1. Try not to over-extend early. Over extension can result in being attacked from multiple fronts. The more enemies you have, the more AI factions [even your allies] are likely to join the feeding frenzy...
2. Defending the seas and fixing bombarded infrastructure in the early game might be an exercise in futility, especially on VH campaign difficulty. Better spend the money on upgrading infrastructure [fields, factories] in provinces that are farther from the coast. You do need a wolf-pack of some stronger ships that to be able to take out an invasion force or two heading your way though. Use gun-boats in strategic straights to scout for those.
3. The economic side of research is extremely important in order to survive (especially on harder campaign difficulties). This should be prioritized early in the campaign. The military side of the research is basically a luxury, kneel fire being an exemption.
4. If you cannot take out your early enemy outright, consider sitting at home with your Daimyo while building up your economy and army and sending a single general (or a couple) into the rear of the enemy territory to burn some infrastructure [unlike for agent sabotages you do not have to pay anything for generals' actions]. Generals do no suffer attrition during winter. After the general has done it's dark deed, hide him in the woods to recycle in the next turn.
5. For assured field victories, get your dirty hands on parrot guns asap...
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