Would knowledge checks made using monster lore suffer from penalties from both wisdom-based checks and intelligence-based checks? If not, which would apply and why? (Assume that the penalties are of different types and sources)
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Student of Philosophy uses the 'in place of' wording, which means that for all effects related to it (including which ability score it is based from), you use Intelligence. Ergo, Family Ties would not apply to it, as Family Ties applies only to charisma or wisdom based checks and Diplomacy is now based on Intelligence.
While a negative Wisdom modifier would be applied to Monster Lore, penalties (such as those from Family Ties) applied to 'wisdom based skill checks' would not. Knowledge is still based on Intelligence in that example (barring other feats or abilities that change it), the character's Wisdom modifier is simply added as a bonus.
In short, if something says 'in place of' it is referring to both what the check is based on and the modifier you use, if something is added as a bonus it doesn't make the check 'based on' anything else, and if the wording says something like 'instead of adding your charisma modifier add your strength modifier on intimidate checks to demoralize' it's more of a grey area - by RAW it hasn't changed what the ability is based on, just which modifier you use for a specific check - by intent, it almost assuredly did mean that it is now Strength-based for that roll.