In both the baptism and the communion question I would have said true to all the questions, except for the ones which implied baptism and communion are symbols. In a very minor sense I suppose they can act as symbols too, but primarly I too think they are "means of grace" which apparently has a different meaning in Lutheran (that's me) and Methodist (yourself, correct?) circles. Or so wikipedia tells me.
The difference is whether something is 'merely symbolic', IMO. I would reject the idea that baptism and communion are merely symbols, but it's pretty hard to deny that they do have very strong symbolic value, as an addition to their main sacramental purposes.
As far as what a means of grace is, the Wikipedia article seems to be more or less correct - that the Methodist view is that said means are the grace imparted through sacraments and those things which God uses to quicken, strengthen, and confirm faith.
Faith, in the Lutheran (we, of course, would argue it's Biblical too) way of thinking, is not a conscious decision but a gift of God. This is huge in how we think about baptism and the Lord's Super. I'm not sure about Methodists, but it seems in the American non-denominational churches, the focus on baptism as a symbol stems from their perception as these sacraments being something that we do - a good work, perhaps. Therefore it's completely foreign to them how anyone could think of Baptism or Communion creating or strengthening a saving faith.
It's both a gift and something of intellectual assent. Only God can save or stir our hearts to redemption, and the sacraments are presented exactly as something that God does rather than something we do. Our growth in faith (or sanctification) after the act of conversion is seen as something in which there is a necessary cooperation between God and Man.
This may get more into the views about soteriology, as Methodism is perhaps the singlemost definitive Arminian (or more precisely, Wesleyan-Arminian) tradition. My understanding of the Lutheran view is that it differs from Calvinism on pretty much the same points that Arminianism does, but the ways it differs is not necessarily the same. So this may have to do with that.
Since it will come up, the Methodist view of grace is one of the central things about it, and makes distinctions between Prevenient, Justifying, and Sanctifying.
Lutherans would hearily agree that good works don't save. What we do believe is that God can use any means to work saving faith in us, and that includes his Word, Baptism and Holy Communion. Because it's God creating faith and not our own intellectual decision, it's perfectly right to expect that God can create saving faith through baptism in a baby, or a person with severe retardation or a disabled stroke victim or anyone without the intellectual brain power to make a decision for Christ. So, in the Lutheran view I would agrue that baptism and communion are infinitely more valuable than they are to those with the symbolic view. Baptism and communion are so much more than intellectual excercises, but a freely given gift of God where work is done in our hearts.
I'm curious what the Methodist view is. You believe that babies should be baptized, but it seems as though you do not think that God can work in us without using the mechanism of our intellect. So I'm wondering what baptism does for babies then.
There is an undercurrent that baptism is the act which removes the stain of Original Sin on the soul and allows for Man's free will to come into effect and seek God. The issue - and this is where Methodism gets kind of muddy - is that the concept of prevenient grace does pretty much the same thing, and said grace is recognized as being given unconditionally to all. This is why I mentioned the part about baptism also being seen as a reflection of that grace, even if the view is that baptism is not what actually imparts prevenient grace, even though - as a sacrament - it is held that baptism does impart grace.
As white dove also noted, the concept of a threshold of accountability plays into it as well. That's not a stated position in the UMC, as far as I'm aware, but it is common to see the idea expressed as God's mercy given to those not able to make that conscious effort.
To be absolutely honest, though, it gets complicated because while Methodism originated in the Church of England and broke away under mainly political pressure (i.e. the American Revolution), it sometimes has a bit of difficulty over whether it wants to be more Anglican or more Protestant. So you'll find some complicated emotions and responses over how to properly understand things like whether baptism removes Original Sin or whether that's already been taken care of due to prevenient grace, or so on. Granted, I'm sure that the official positions have these things sorted out, but Methodism is often one of the least understood traditions in Protestantism, for those outside of it and many times even for those inside of it. The 200+ year separation from Anglicanism has also lead to inevitable drift in some areas, and this drift is typically not very uniform.
